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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