Q. 555.0( 1 Vote )

# If matrix <

Answer :

We are given that, A2 = pA

We need to find the value of p.

First, let us find A2.

We know that, A2 = A.A In multiplication of matrices A and A, such that A2 = Z(say): For the calculation of z11: Dot multiply the 1st row of first matrix and the 1st column of second matrix and then sum up.

(2 -2)(2 -2) = 2 × 2 + (-2) × (-2)

(2 -2)(2 -2) = 4 + 4

(2 -2)(2 -2) = 8

So, For the calculation of z12: Dot multiply the 1st row of first matrix and the 2nd column of second matrix and then sum up.

(2 -2)(-2 2) = 2 × -2 + (-2) × 2

(2 -2)(-2 2) = -4 – 4

(2 -2)(-2 2) = -8

So, Similarly,   So, …(i)

Now, let us find pA.

Multiply p by matrix A,   …(ii)

Substituting value of A2 and pA from (i) and (ii) in

A2 = pA We know by the property of matrices, This implies,

a11 = b11, a12 = b12, a21 = b21 and a22 = b22

So,

2p = 8

-2p = -8

-2p = -8

2p = 8

Take equation,

2p = 8 p = 4

Thus, the value of p = 4.

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