NCERT solutions for class 12 maths exercise 3.2 of chapter 3-Matrices

NCERT solutions for class 12 maths exercise 3.2 of chapter 3-Matrices are very important not only to the class 12 CBSE students but also for the students who are going to appear in the entrance exam of engineering, NDA, and CDS. NCERT solutions for class 12 maths exercise 3.2 of chapter 3-Matrices are created here for clearing the doubts of students in chapter 3-Matrices for a better understanding of the concept which is required to solve the questions in the exam.NCERT solutions for class 12 maths exercise 3.2 of chapter 3-Matrices are solved by an expert of the subject.

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lutions for class 12 maths exercise 3.2 of chapter 3-Matrices are the solutions of all unsolved questions of exercise 3.2 of chapter 3-Matrices of the NCERT maths textbook. Matrix has huge applications in the field of business, economics, architect, geology, engineering and science, and technology. Here in this exercise, you will learn multiplication, division, addition, and subtraction of Matrices.

NCERT solutions for class 12 maths exercise 3.1 of chapter 3-Matrices

NCERT solutions of class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Study notes of Maths and Science NCERT and CBSE from class 9 to 12

NCERT solutions for class 12 maths exercise 3.2 of chapter 3-Matrices

Q1.

$Let\: A= \begin{bmatrix}2 &4 \\ 3& 2 \end{bmatrix},B=\begin{bmatrix}1 & 3\\ -2&5 \end{bmatrix},C=\begin{bmatrix}-2 &5 \\ 3 & 4 \end{bmatrix}$

Find each of the following.

(i) A + B (ii) A – B (iii) 3A – C (iv) AB (v) BA

Ans. (i) A + B

$=\begin{bmatrix}2 &4 \\ 3& 2 \end{bmatrix}+\begin{bmatrix}1 & 3\\ -2&5 \end{bmatrix}$

$=\begin{bmatrix}2+1 & 4+3\\ 3-2&2+5 \end{bmatrix}$

$=\begin{bmatrix}3 & 7\\ 1&7 \end{bmatrix}$

(ii) A – B

$=\begin{bmatrix}2 & 4\\ 3&2 \end{bmatrix}-\begin{bmatrix}1 & 3\\ -2&5 \end{bmatrix}$

$=\begin{bmatrix}2-1 & 4-3\\ 3+2&2-5 \end{bmatrix}$

$=\begin{bmatrix}1 & 1\\ 5&-3 \end{bmatrix}$

(iii) 3A – C

$=\begin{bmatrix}2 &4 \\ 3 & 2 \end{bmatrix}\begin{bmatrix}1 & 3\\ -2 & 5 \end{bmatrix}$

$=\begin{bmatrix}6 & 12\\ 9& 6 \end{bmatrix}-\begin{bmatrix}-2 &5 \\ 3& 4 \end{bmatrix}$

$=\begin{bmatrix}6+2 & 12-5\\ 9-3& 6-4 \end{bmatrix}$

(iv) AB

$=\begin{bmatrix}2 &4 \\ 3 & 2 \end{bmatrix}\begin{bmatrix}1 & 3\\ -2 & 5 \end{bmatrix}$

$=\begin{bmatrix}2\times 1+4\times -2 & 2\times 3+4\times 5\\ 3\times 1+2\times -2 & 3\times 3+2\times 5 \end{bmatrix}$

$=\begin{bmatrix} -6 & 26\\ -1 & 19 \end{bmatrix}$

(v) BA

$=\begin{bmatrix} 1 & 3\\ -2 & 5 \end{bmatrix}\begin{bmatrix}2 &4 \\ 3 & 2 \end{bmatrix}$

$=\begin{bmatrix}1\times 2+3\times 3 &1\times 4+3\times 2 \\ -2\times 2+5\times 3& -2\times 4+5\times 2 \end{bmatrix}$

$=\begin{bmatrix}11 &10 \\ 11& 2 \end{bmatrix}$

Q2. Compute the following

$\left ( i \right )\begin{bmatrix}a &b \\ -b& a \end{bmatrix}+\begin{bmatrix}a & b\\ b& a \end{bmatrix}$ $\left ( ii \right )\begin{bmatrix}a^{2}+b^{2} &b^{2}+c^{2} \\ a^{2}+c^{2}& a^{2}+b^{2} \end{bmatrix}+\begin{bmatrix}2ab & 2bc\\ -2ac& -2ab \end{bmatrix}$

$\left ( iii \right )\begin{bmatrix}-1 &4 & -6\\ 8 & 5 & 16\\ 2 & 8 & 5 \end{bmatrix}+\begin{bmatrix}12 &7 &6 \\ 8&0 & 5\\ 3 & 2 & 4 \end{bmatrix}$ $\left ( iv \right )\begin{bmatrix}cos^{2}x &sin^{2}x \\ sin^{2}x& cos^{2}x \end{bmatrix}+\begin{bmatrix}sin^{2}x &cos^{2}x \\ cos^{2}x& sin^{2}x \end{bmatrix}$

Ans.

$\left ( i \right )\begin{bmatrix}a &b \\ -b& a \end{bmatrix}+\begin{bmatrix}a & b\\ b& a \end{bmatrix}$

$=\begin{bmatrix}a+a &b+b \\ -b+b& a+a \end{bmatrix}=\begin{bmatrix}2a & 2b\\ 0 & 2a \end{bmatrix}$

$\left ( ii \right )\begin{bmatrix}a^{2}+b^{2} &b^{2}+c^{2} \\ a^{2}+c^{2}& a^{2}+b^{2} \end{bmatrix}+\begin{bmatrix}2ab & 2bc\\ -2ac& -2ab \end{bmatrix}$

$=\begin{bmatrix}a^{2}+b^{2}+2ab & b^{2}+c^{2}+2bc\\ a^{2}+c^{2}-2ac& a^{2}+b^{2}-2ab \end{bmatrix}=\begin{bmatrix}\left ( a+b \right )^{2} &\left ( b+c \right )^{2} \\ \left ( a-c \right )^{2} & \left ( a-b \right )^{2} \end{bmatrix}$

$\left ( iii \right )\begin{bmatrix}-1 &4 & -6\\ 8 & 5 & 16\\ 2 & 8 & 5 \end{bmatrix}+\begin{bmatrix}12 &7 &6 \\ 8&0 & 5\\ 3 & 2 & 4 \end{bmatrix}$

$=\begin{bmatrix}-1+12 &4+7 & -6+6\\ 8+8 & 5+0 & 16+5\\ 2+3 &8+2 & 5+4 \end{bmatrix}=\begin{bmatrix}11 & 11 & 0\\ 16 & 5 & 21\\ 5 & 10 & 9 \end{bmatrix}$

$\left ( iv \right )\begin{bmatrix}cos^{2}x &sin^{2}x \\ sin^{2}x& cos^{2}x \end{bmatrix}+\begin{bmatrix}sin^{2}x &cos^{2}x \\ cos^{2}x& sin^{2}x \end{bmatrix}$

$=\begin{bmatrix}cos^{2}x+sin^{2}x &sin^{2}x+cos^{2}x \\ sin^{2}x+cos^{2}x& cos^{2}x+sin^{2}x \end{bmatrix}=\begin{bmatrix}1 &1 \\ 1& 1 \end{bmatrix}$

Q3. Compute the indicated products

$\left ( i\right )\begin{bmatrix}a &b \\ -b & a \end{bmatrix}\begin{bmatrix}a & -b\\ b& a \end{bmatrix}$ $\left ( ii \right )\begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}\begin{bmatrix}2 & 3 & 4 \end{bmatrix}$

$\left ( iii \right )\begin{bmatrix}1 & -2\\ 2& 3 \end{bmatrix}\begin{bmatrix}1 & 2 & 3\\ 2& 3& 1 \end{bmatrix}$ $\left ( iv \right )\begin{bmatrix}2 & 3 & 4\\ 3&4 &5 \\ 4& 5& 6 \end{bmatrix}\begin{bmatrix}1 & -3 & 5\\ 0& 2 & 4\\ 3& 0 & 5 \end{bmatrix}$

$\left ( v \right )\begin{bmatrix}2 &1 \\ 3&2 \\ -1& 1 \end{bmatrix}\begin{bmatrix}1 & 0 & 1\\ -1& 2 & 1 \end{bmatrix}$ $\left ( vi \right )\begin{bmatrix}3 & -1 &3 \\ -1& 0& 2 \end{bmatrix}\begin{bmatrix}2 &-3 \\ 1 & 0\\ 3& 1 \end{bmatrix}$

Ans.

$\left ( i\right )\begin{bmatrix}a &b \\ -b & a \end{bmatrix}\begin{bmatrix}a & -b\\ b& a \end{bmatrix}$

$=\begin{bmatrix}a^{2}+b^{2} & -ab+ba\\ -ab+ab& b^{2}+a^{2} \end{bmatrix}=\begin{bmatrix}a^{2}+b^{2} &0 \\ 0& b^{2}+a^{2} \end{bmatrix}$

Ans.

$\left ( i\right )\begin{bmatrix}a &b \\ -b & a \end{bmatrix}\begin{bmatrix}a & -b\\ b& a \end{bmatrix}$

$=\begin{bmatrix}a^{2}+b^{2} & -ab+ba\\ -ab+ab& b^{2}+a^{2} \end{bmatrix}=\begin{bmatrix}a^{2}+b^{2} &0 \\ 0& b^{2}+a^{2} \end{bmatrix}$

$\left ( ii \right )\begin{bmatrix}1 \\ 2 \\ 3 \end{bmatrix}\begin{bmatrix}2 & 3 & 4 \end{bmatrix}$

$=\begin{bmatrix}1\times 2 & 1\times 3 & 1\times 4\\ 2\times 2& 2\times 3 &2\times 4 \\ 3\times 2 &3\times 3 & 3\times 4 \end{bmatrix}=\begin{bmatrix}2 &3 & 4\\ 4& 6 & 8\\ 6& 9 & 12 \end{bmatrix}$

$\left ( iii \right )\begin{bmatrix}1 & -2\\ 2& 3 \end{bmatrix}\begin{bmatrix}1 & 2 & 3\\ 2& 3& 1 \end{bmatrix}$

$=\begin{bmatrix}1\times 1-2\times 2 & 1\times 2 -2\times 3&1\times 3-2\times 1 \\ 2\times 1+3\times 2&2\times 2+3\times 3 &2\times 3+3\times 1 \end{bmatrix}=\begin{bmatrix}-3 &-4 & 1\\ 8 &13 & 9 \end{bmatrix}$

$\left ( iv \right )\begin{bmatrix}2 & 3 & 4\\ 3&4 &5 \\ 4& 5& 6 \end{bmatrix}\begin{bmatrix}1 & -3 & 5\\ 0& 2 & 4\\ 3& 0 & 5 \end{bmatrix}$

$=\begin{bmatrix}2\times 1+3\times 0+4\times 3 & 2\times -3 +3\times 2+4\times 0&2\times 5+3\times 4+4\times 5 \\ 3\times 1+4\times0 +5\times 3 & 3\times -3+4\times 2+5\times 0 &3\times 5+4\times 4+5\times 5 \\ 4\times 1+5\times 0+6\times 3 &4\times -3+5\times 2+6\times 0 &4\times 5+5\times 4+6\times 5 \end{bmatrix}$

$=\begin{bmatrix}14 &0 &42 \\ 18& -1 &56 \\ 22 & -2 & 70 \end{bmatrix}$

$\left ( v \right )\begin{bmatrix}2 &1 \\ 3&2 \\ -1& 1 \end{bmatrix}\begin{bmatrix}1 & 0 & 1\\ -1& 2 & 1 \end{bmatrix}$

$=\begin{bmatrix}2\times 1+1\times -1 & 2\times 0+1\times 2 & 2\times 1+1\times 1\\ 3\times 1+2\times -1&3\times 0+2\times 2 &3\times 1+2\times 1 \\ -1\times 1+1\times -1&-1\times 0+1\times 2 & -1\times 1+1\times 1 \end{bmatrix}$

$=\begin{bmatrix}1 & 2 &3 \\ 1& 4 & 5\\ -2& 2 & 0 \end{bmatrix}$

$\left ( vi \right )\begin{bmatrix}3 & -1 &3 \\ -1& 0& 2 \end{bmatrix}\begin{bmatrix}2 &-3 \\ 1 & 0\\ 3& 1 \end{bmatrix}$

$=\begin{bmatrix}3\times 2-1\times 1+3\times 3 &3\times -3 -1\times 0+3\times 1\\ -1\times 2+0\times 1+2\times 3& -1\times -3+0\times 0+2\times 1 \end{bmatrix}$

$=\begin{bmatrix}14 &-6 \\ 4& 5 \end{bmatrix}$

Q4. If

$A=\begin{bmatrix}1 &2 &-3 \\ 5&0 &2 \\ 1 & -1 & 1 \end{bmatrix},B=\begin{bmatrix}3 & -1 & 2\\ 4& 2&5 \\ 2& 0 & 3 \end{bmatrix}\: and\:C= \begin{bmatrix}4 & 1& 2\\ 0& 3 & 2\\ 1 & -2 & 3 \end{bmatrix}$

Then compute ,(A +B) and (B – C). Also verify that A + (B – C) = (A + B) – C

Ans.

A + B

$=\begin{bmatrix}1 & 2 &-3 \\ 5& 0 & 2\\ 1& -1 & 1 =\end{bmatrix}+\begin{bmatrix}3 &-1 &2 \\ 4&2 &5 \\ 2&0 & 3 \end{bmatrix}=\begin{bmatrix}1+3 &2-1 &-3+2 \\ 5+4& 0+2 &2+5 \\ 1+2 &-1+0 &1+ 3 \end{bmatrix}=\begin{bmatrix}4 & 1 &-1 \\ 9& 2 & 7\\ 3& -1 & 4 \end{bmatrix}$

(B – C)

$=\begin{bmatrix}3 & -1 &2 \\ 4& 2 &5\\ 2& 0 & 3 \end{bmatrix}-\begin{bmatrix}4 & 1& 2\\ 0& 3& 2\\ 1& -2& 3 \end{bmatrix}=\begin{bmatrix}3-4 &-1-1 &2-2 \\ 4-0& 2-3 &5-2 \\ 2-1& 0+2& 3-3 \end{bmatrix}=\begin{bmatrix}-1 & -2 & 0\\ 4& -1 & 3\\ 1& 2&0 \end{bmatrix}$

Now,we have to verify that A + (B – C) = (A + B) – C

LHS , A + (B – C) , Putting the value of A and (B – C)

$=\begin{bmatrix}1 & 2 &-3 \\ 5& 0 &2\\ 1& -1 & 1 \end{bmatrix}+\begin{bmatrix}-1 & -2 & 0\\ 4& -1 & 3\\ 1& 2&0 \end{bmatrix}=\begin{bmatrix}1-1 & 2-2 &-3+0 \\ 5+4& 0-1 & 2+3\\ 1+1&-1+2 & 1+0 \end{bmatrix}=\begin{bmatrix}0 & 0 & -3\\ 9& -1 &5 \\ 2& 1 & 1 \end{bmatrix}$

RHS , (A + B) – C , Putting the value of C and (A+B )

$\begin{bmatrix}4 & 1 &-1 \\ 9 & 2 &7 \\ 3 & -1& 4 \end{bmatrix}-\begin{bmatrix}4 & 1 &2 \\ 0& 3 & 2\\ 1& -2 & 3 \end{bmatrix}=\begin{bmatrix}4-4 & 1-1 & -1-2\\ 9-0& 2-3 &7-2 \\ 3-1& -1+2 & 4-3 \end{bmatrix}=\begin{bmatrix}0 & 0 &-3 \\ 9 & -1 & 5\\ 2&1 & 1 \end{bmatrix}$

Therefore , LHS = RHS, Verified

$Q5.If\: A=\begin{bmatrix}2/3 & 1 &5/3 \\ 1/3 &2/3 & 4/3\\ 7/3& 2& 2/3 \end{bmatrix}\: and\: B=\begin{bmatrix}2/5 & 3/5 &1 \\ 1/5& 2/5 & 4/5\\ 7/5& 6/5 & 2/5 \end{bmatrix}$

Then compute 3A – 5B

Ans. We have to get the value of 3A – 5B

$\: 3A-5B=3\begin{bmatrix}2/3 & 1 &5/3 \\ 1/3 &2/3 & 4/3\\ 7/3& 2& 2/3 \end{bmatrix}\: -\: 5\begin{bmatrix}2/5 & 3/5 &1 \\ 1/5& 2/5 & 4/5\\ 7/5& 6/5 & 2/5 \end{bmatrix}$

$=\begin{bmatrix}2 & 3 &5 \\ 1 &2 & 4\\ 7& 6& 2 \end{bmatrix}\: -\: \begin{bmatrix}2 & 3 &5 \\ 1& 2& 4\\ 7& 6 & 2 \end{bmatrix}=\begin{bmatrix}2-2 &3-3 &5-5 \\ 1-1&2-2 &4-4 \\ 7-7 & 6-6 & 2-2 \end{bmatrix}=\begin{bmatrix}0 &0 &0 \\ 0 &0 & 0\\ 0 &0 & 0 \end{bmatrix}=0$

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Q6. Simplify

$cos\Theta \begin{bmatrix}cos\Theta &sin\Theta \\ -sin\Theta & cos\Theta \end{bmatrix}+sin\Theta \begin{bmatrix}sin\Theta & -cos\Theta \\ cos\Theta & sin\Theta \end{bmatrix}$

Ans. We are given the expression

$cos\Theta \begin{bmatrix}cos\Theta &sin\Theta \\ -sin\Theta & cos\Theta \end{bmatrix}+sin\Theta \begin{bmatrix}sin\Theta & -cos\Theta \\ cos\Theta & sin\Theta \end{bmatrix}$

Simplifying it

$=\begin{bmatrix}cos^{2}\Theta &sin\Theta.cos\Theta \\ -sin\Theta.cos\Theta & cos^{2}\Theta \end{bmatrix}+ \begin{bmatrix}sin^{2}\Theta & -cos\Theta.sin\Theta \\ cos\Theta .sin\Theta & sin^{2}\Theta \end{bmatrix}$

$\begin{bmatrix}cos^{2}\Theta +sin^{2}\Theta & sin\Theta .cos\Theta -cos\Theta .sin\Theta \\ -sin\Theta .cos\Theta+cos\Theta .sin\Theta & cos^{2}\Theta +sin^{2}\Theta \end{bmatrix}$

$=\begin{bmatrix}1 &0 \\ 0& 1 \end{bmatrix}=I$

Where I mean unit matrix

Q7. Find X and Y if

$\left ( i \right )X +Y=\begin{bmatrix}7 &0 \\ 2& 5 \end{bmatrix}\: and\: X-Y=\begin{bmatrix}3 & 0\\ 0& 3 \end{bmatrix}$

$\left ( ii \right )2X +3Y=\begin{bmatrix}2 &3 \\ 4& 0 \end{bmatrix}\: and\: 3X+2Y=\begin{bmatrix}2 & -2\\ -1& 5 \end{bmatrix}$

Ans.

(i) We are given

$X +Y=\begin{bmatrix}7 &0 \\ 2& 5 \end{bmatrix}...\left ( 1 \right ) , X-Y=\begin{bmatrix}3 & 0\\ 0& 3 \end{bmatrix}....\left ( 2 \right )$

Adding both equations (i) and (ii),we have

$2X =\begin{bmatrix}7 &0 \\ 2& 5 \end{bmatrix}+ \begin{bmatrix}3 & 0\\ 0& 3 \end{bmatrix}=\begin{bmatrix}10 & 0\\ 2 &8 \end{bmatrix}$

$X= \frac{1}{2}\begin{bmatrix}10 & 0\\ 2& 8 \end{bmatrix}$

$X= \begin{bmatrix}5 & 0\\ 1& 4 \end{bmatrix}$

Putting the value of X in equation (i)

$\begin{bmatrix}5 &0 \\ 1& 4 \end{bmatrix}+Y=\begin{bmatrix}7 & 0\\ 2& 5 \end{bmatrix}$

$Y=\begin{bmatrix}7 & 0\\ 2& 5 \end{bmatrix}-\begin{bmatrix}5 &0 \\ 1& 4 \end{bmatrix}=\begin{bmatrix}2 & 0\\ 1&1 \end{bmatrix}$

(ii) We are given

$2X+3Y=\begin{bmatrix}2 & 3\\ 4& 0 \end{bmatrix}...\left ( 1 \right ),3X+2Y=\begin{bmatrix}2 &-2 \\ -1& 5 \end{bmatrix}....\left ( 2 \right )$

Multiplying equation (1) by 3 and equation (2) by 2, we get equation (3) and equation (4)

(i) We are given

$6X+9Y=\begin{bmatrix}6 & 9\\ 12& 0 \end{bmatrix}...\left ( 3 \right ),6X+4Y=\begin{bmatrix}4 &-4 \\ -2& 10 \end{bmatrix}....\left ( 4 \right )$

Subtracting equation (4) from equation (3)

$5y=\begin{bmatrix}2 &13 \\ 14& -10 \end{bmatrix}$

$y=\begin{bmatrix}2/5 &13/5 \\ 14/5& -2 \end{bmatrix}$

Putting the value of Y in equation (i)

$2X +3\begin{bmatrix}2/5 &13/5 \\ 14/5 & -2 \end{bmatrix}=\begin{bmatrix}2 & 3\\ 4& 0 \end{bmatrix}$

$2X +\begin{bmatrix}6/5 &39/5 \\ 42/5 & -6 \end{bmatrix}=\begin{bmatrix}2 & 3\\ 4& 0 \end{bmatrix}$

$2X =\begin{bmatrix}2 & 3\\ 4& 0 \end{bmatrix}-\begin{bmatrix}6/5 &39/5 \\ 42/5 & -6 \end{bmatrix}$

$2X =\begin{bmatrix}4/5 &-24/5 \\ -22/5 & 6 \end{bmatrix}$

$X =\begin{bmatrix}2/5 &-12/5 \\ -11/5 & 3 \end{bmatrix}$

Q8. Find X, if

$Y=\begin{bmatrix}3 &2 \\ 1 & 4 \end{bmatrix}\: and\: 2X +Y=\begin{bmatrix}1 &0 \\ -3& 2 \end{bmatrix}$

Ans. We are given

$2X +Y=\begin{bmatrix}1 &0 \\ -3& 2 \end{bmatrix}....\left ( 1 \right )$

$Y=\begin{bmatrix}3 &2 \\ 1 & 4 \end{bmatrix}\:$

Putting the value of Y in equation (i)

$2X+ \begin{bmatrix}3 & 2\\ 1& 4 \end{bmatrix}=\begin{bmatrix}1 &0 \\ -3& 2 \end{bmatrix}$

$2X =\begin{bmatrix}1 &0 \\ -3& 2 \end{bmatrix}-\begin{bmatrix}3 & 2\\ 1& 4 \end{bmatrix}=\begin{bmatrix}-2 & -2\\ -4 & -2 \end{bmatrix}$

$X=\begin{bmatrix}-1 & -1\\ -2 & -1 \end{bmatrix}$

Q9. Find X and Y, if

$2\begin{bmatrix}1 & 3\\ 0 & x \end{bmatrix}+\begin{bmatrix}y &0 \\ 1 & 2 \end{bmatrix}=\begin{bmatrix}5 &6 \\ 1& 8 \end{bmatrix}$

$\begin{bmatrix}2 & 6\\ 0 & 2x \end{bmatrix}+\begin{bmatrix}y &0 \\ 1 & 2 \end{bmatrix}=\begin{bmatrix}5 &6 \\ 1& 8 \end{bmatrix}$

$\begin{bmatrix}2+y & 6\\ 1 & 2x+2 \end{bmatrix}=\begin{bmatrix}5 &6 \\ 1& 8 \end{bmatrix}$

Two matrices are equal indicates that their corresponding elements would be equal.

2+ y = 5⇒ y = 5 – 2 = 3

2x + 2 = 8

2x = 8 – 2 = 6

x = 3

Hence x = 3 and y = 3

Q10. Solve the equation for x,y,z and t,if

$2\begin{bmatrix}x & z\\ y & t \end{bmatrix}+3\begin{bmatrix}1 & -1\\ 0& 2 \end{bmatrix}=3\begin{bmatrix}3 & 5\\ 4 & 6 \end{bmatrix}$

Ans. We are given that

$2\begin{bmatrix}x & z\\ y & t \end{bmatrix}+3\begin{bmatrix}1 & -1\\ 0& 2 \end{bmatrix}=3\begin{bmatrix}3 & 5\\ 4 & 6 \end{bmatrix}$

Simplifying LHS and RHS

$\begin{bmatrix}2x & 2z\\ 2y & 2t \end{bmatrix}+\begin{bmatrix}3 & -3\\ 0& 6 \end{bmatrix}=\begin{bmatrix}9 & 15\\ 12 & 18 \end{bmatrix}$

$\begin{bmatrix}2x+3 & 2z-3\\ 2y & 2t+6 \end{bmatrix}=\begin{bmatrix}9 & 15\\ 12 & 18 \end{bmatrix}$

Two matrices are equal indicates that their corresponding elements would be equal.

2x + 3 = 9 ⇒2 x = 9- 3 = 6 ⇒x = 3

2z – 3 = 15⇒ 2z = 15+ 3= 18 ⇒ z = 9

2y = 12 ⇒ y = 6

2t + 6 = 18 ⇒ 2t = 18 – 6 = 12⇒ t = 6

Hence value of x= 3, y= 6,z= 9 and t = 6

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals	Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds	Chapter 12- Electricity
Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process	Chapter 14-Sources of Energy
Chapter 7-Control and Coordination	Chapter 15-Environment
Chapter 8- How do organisms reproduce?	Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions for class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals