**Chapter 4 Determinants and Matrices Ex 4.6**

## Chapter 4 Determinants and Matrices Ex 4.6

**Question 1.Evaluate:**

**Question 2.Solution:**

From (i) and (ii), we get

AB â‰ BA

**Question 3.**

**answer.Solution:**

From (i) and (ii), we get

AB â‰ BA

**Question 4.Show that AB = BA, whereSolution:**

From (i) and (ii), we get

AB = BA

From (i) and (ii), we get

AB = BA

[Note: The question has been modified.]

**Question 5.**

**Solution:**

From (i) and (ii), we get

A(BC) = (AB)C.

**Question 7.Verify that A(B + C) = AB + AC in each of the following matrices:Solution:**

From (i) and (ii), we get

A(B + C) = AB + AC.

[Note: The question has been modified.]

**Question 8.Solution:**

**Question 9.Solution:**

im

âˆ´ AB is non-singular matrix.

**Question 10.If A = , find the product (A + I)(A â€“ I).Solution:**

âˆ´ By equality of matrices, we get

= 1 and Î± + 1 = 2

âˆ´ Î± = Â± 1 and Î± = 1

âˆ´ Î± = 1

**Question 12.**

**Solution:**

â€“ 4A = A.A â€“ 4A

**Question 13.Solution:**

â€“ 8A â€“ kI = O

âˆ´ A.A â€“ 8A â€“ kI = O

âˆ´ by equality of matrices, we get

1 â€“ 8 â€“ k = 0

âˆ´ k = -7

**Question 14.Solution:**

â€“ 5A + 7I = 0 = A.A â€“ 5A + 7I = 0

**Question 16.**

From (i) and (ii), we get AB = BA

**Question 17.**

âˆ´ by equality of matrices, we get

â€“ 2 + a = 0 and 1 + b = 0

a = 2 and b = -1

[Note: The question has been modified.]

**Question 18.Find matrix X such that AX = B,**

**Question 19.Solution:**

= kA â€“ 2I

âˆ´ AA + 2I = kA

âˆ´ By equality of matrices, we get

3k = 3

âˆ´ k = 1

**Question 20.Solution:**

âˆ´ [6 + 12x + 14] =[0]

âˆ´ By equality of matrices, we get

âˆ´ 12x + 20 = 0

âˆ´ 12x =-20

âˆ´ x = -5/3

**Question 21.Solution:**

âˆ´ By equality of matrices, we get

x = 19 andy = 12

**Question 22.Find x, y, z ifSolution:**

âˆ´ By equality of matrices, we get

x â€“ 3 = -6,y â€“ 1 = 0, 2z = -2

âˆ´ x = â€“ 3, y = 1, z = â€“ 1

**Question 23.Solution:**

**Question 24.**

**Question 25.Jay and Ram are two friends in a class. Jay wanted to buy 4 pens and 8 notebooks, Ram wanted to buy 5 pens and 12 notebooks. Both of them went to a shop. The price of a pen and a notebook which they have selected was 6 and â‚¹ 10. Using matrix multiplication, find the amount required from each one of them.Solution:**

Let A be the matrix of pens and notebooks and B be the matrix of prices of one pen and one notebook.

The total amount required for each one of them is obtained by matrix AB.

âˆ´ Jay needs â‚¹ 104 and Ram needs â‚¹ 150.