NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.2 are part of NCERT Solutions for Class 12 Maths . Here we have given NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Matrices |

Exercise |
Ex 3.2 |

Number of Questions Solved |
22 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.2

**Ex 3.2 Class 12 Maths Question 1.**

**Let **

**Find each of the following:**

**(i) A + B**

**(ii) A – B**

**(iii) 3A – C**

**(iv) AB**

**(v) BA**

**Solution:**

Let

(i) A + B

**Ex 3.2 Class 12 Maths Question 2.**

**Compute the following:**

**Solution:**

**Ex 3.2 Class 12 Maths Question 3.**

**Compute the indicated products.**

**(i) **

**(ii) **

**(iii) **

**(iv) **

**(v) **

**(vi) **

**Solution:**

(i)

=

**Ex 3.2 Class 12 Maths Question 4.**

**If **

**then compute (A + B) and (B – C). Also verify that A + (B – C) = (A + B) – C.**

**Solution:**

Given

**Ex 3.2 Class 12 Maths Question 5.**

**If **

**then compute 3A – 5B.**

**Solution:**

=

**Ex 3.2 Class 12 Maths Question 6.**

**Simplify:**

**Solution:**

**Ex 3.2 Class 12 Maths Question 7.**

**Find X and Y if**

**Solution:**

**Ex 3.2 Class 12 Maths Question 8.**

**Find**

**Solution:**

We are given that

**Ex 3.2 Class 12 Maths Question 9.**

**Find x and y, if **

**Solution:**

=>

=> 2+y = 5 and 2x+2 = 8

=> y=3 and x=3

Hence x=3 and y=3

**Ex 3.2 Class 12 Maths Question 10.**

**Solve the equation for x,y,z and t, if**

**Solution:**

**Ex 3.2 Class 12 Maths Question 11.**

**If then find the values of x and y**

**Solution:**

=>

**Ex 3.2 Class 12 Maths Question 12.**

**Given**

**find the values of x,y,z and w.**

**Solution:**

=>

=> 3x = x + 4 => x = 2

and 3y = 6 + x + y => y = 4

Also, 3w = 2w + 3 => w = 3

Again, 3z = – 1 + z + w

=> 2z = – 1 + 3

=> 2z = 2

=> z = 1

Hence x = 2 ,y = 4, z = 1, w = 3.

**Ex 3.2 Class 12 Maths Question 13.**

**If F(x) = **

**then show that F(x).F(y) = F(x+y)**

**Solution:**

F(x) =

∴ F(y) =

**Ex 3.2 Class 12 Maths Question 14.**

**Show that**

**Solution:**

L.H.S≠R.H.S

**Ex 3.2 Class 12 Maths Question 15.**

**Find A² – 5A + 6I, if A = **

**Solution:**

A² – 5A + 6I =

**Ex 3.2 Class 12 Maths Question 16.**

**If A = Prove that A³-6A²+7A+2I = 0**

**Solution:**

We have

A² = A x A

=

**Ex 3.2 Class 12 Maths Question 17.**

**If then ****find k so that A²=kA-2I**

**Solution:**

Given

Required: To find the value of k

Now A²=kA-2I

**Ex 3.2 Class 12 Maths Question 18.**

**If and I is the identity matrix of order 2,show that**

**Solution:**

L.H.S=

**Ex 3.2 Class 12 Maths Question 19.**

**A trust has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year and second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bond if the trust fund obtains an annual total interest of**

**(a) Rs 1800**

**(b) Rs 2000**

**Solution:**

Let Rs 30,000 be divided into two parts and Rs x and Rs (30,000-x)

Let it be represented by 1 x 2 matrix [x (30,000-x)]

Rate of interest is 005 and 007 per rupee.

It is denoted by the matrix R of order 2 x 1.

**Ex 3.2 Class 12 Maths Question 20.**

**The book-shop of a particular school has 10 dozen Chemistry books, 8 dozen Physics books, 10 dozen Economics books. Their selling price are Rs 80, Rs 60 and Rs 40 each respectively. Find die total amount the book-shop will receive from selling all the books using matrix algebra.**

**Solution:**

Number of Chemistry books = 10 dozen books

= 120 books

Number of Physics books = 8 dozen books = 96 books

Number of Economics books = 10 dozen books

= 120 books

**Assuming X, Y, Z, W and P are the matrices of order 2 x n, 3 x k, 2 x p, n x 3 and p x k respectively. Choose the correct answer in Question 21 and 22.**

**Ex 3.2 Class 12 Maths Question 21.**

**The restrictions on n, k and p so that PY + WY will be defined are**

**(a) k = 3 ,p = n**

**(b) k is arbitrary,p = 2**

**(c) pis arbitrary, k = 3**

**(d) k = 2,p = 3**

**Solution:**

Given : x_{2xn,} y_{3xn}, z_{2xp,} w_{nx3, }P_{pxk}

Now py +wy = P_{pxk} x y_{3+k} x w_{nx3} x y_{3xk}

Clearly, k = 3 and p = n

Hence, option (a) is correct p x 2.

**Ex 3.2 Class 12 Maths Question 22.**

**If n = p, then the order of the matrix 7X – 5Z is:**

**(a) p x 2**

**(b) 2 x n**

**(c) n x 3**

**(d) p x n.**

**Solution:**

7X – 5Z = 7X_{2xn} – 5X_{2xp}

∴ We can add two matrices if their order is same n = P

∴ Order of 7X – 5Z is 2 x n.

Hence, option (b) is correct 2 x n.

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