Q. 635.0( 1 Vote )

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Answer :

We are given that, We need to find the value of (x, y).

Multiply the matrices on the right hand side of the equation, For z11: Dot multiply the 1st row of first matrix and 1st column of second matrix, then sum up.

(2 1)(1 -2) = 2 × 1 + 1 × -2

(2 1)(1 -2) = 2 – 2

(2 1)(1 -2) = 0

So, For z21: Dot multiply the 2nd row of first matrix and 1st column of second matrix, then sum up.

(4 3)(1 -2) = 4 × 1 + 3 × (-2)

(4 3)(1 -2) = 4 – 6

(4 3)(1 -2) = -2

So, Equate the resulting matrix to the given matrix equation.  We know by the property of matrices, This implies,

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

Therefore,

x + y = 0

x – y = -2

Adding these two equations, we get

(x + y) + (x – y) = 0 + (-2)

x + y + x – y = -2

x + x + y – y = -2

2x + 0 = -2

2x = -2 x = -1

Putting x = -1 in

x + y = 0

(-1) + y = 0

-1 + y = 0

y = 1

So, putting values of x and y from above in (x, y), we get

(x, y) = (-1, 1)

Thus, (x, y) is (-1, 1).

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