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

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

ncert solutions exercise 3.2 matrices

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

ncert solutions exercise 3.2 matrices

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 FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE 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.

Find each of the following.

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

Ans. (i) A + B

(ii)  A – B

(iii)  3A – C

(iv) AB

 

(v) BA

Q2. Compute the following

 

           

         

Ans.

Q3. Compute the indicated products

     

 

   

       

Ans.

Ans.

 

Q4. If

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

Ans.

A + B

(B – C)

 

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

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

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

Therefore , LHS = RHS, Verified

Then compute 3A – 5B

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

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Q6. Simplify

Ans.  We are given the expression

Simplifying it

 

 

Where I mean unit matrix

Q7. Find X and Y if

Ans.

(i) We are given

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

Putting the value of X in equation (i)

(ii) We are given

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

(i) We are given

 

Subtracting equation   (4) from equation (3)

Putting the value of Y in equation (i)

Q8. Find X, if

Ans. We are given

Putting the value of Y  in equation  (i)

 

Q9. Find X and Y, if

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

Ans. We are given that

Simplifying LHS and RHS

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 SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

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NCERT Solutions for Class 10 Science

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

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 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 FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution

 

 

 

 

 

 

 

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