**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**

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.

NCERT solutions 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.

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 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 |

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**NCERT solutions of 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 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 |

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