Answer :

We are given with


We need to find the value of k.


Take Left Hand Side (LHS) of the matrix equation.



In multiplication of matrices,



For c11: dot multiply the matching members of 1st row of first matrix and 1st column of second matrix and then sum up.


(a11 a12)(b11 b21) = a11 × b11 + a12 × b21


Thus,


(1 2)(3 2) = 1 × 3 + 2 × 2


(1 2)(3 2) = 3 + 4


(1 2)(3 2) = 7



For c12: dot multiply the matching members of 1st row of first matrix and 2nd column of second matrix and then sum up.


(a11 a12)(b12 b22) = a �11 × b12 + a12 × b22


Thus,


(1 2)(1 5) = 1 × 1 + 2 × 5


(1 2)(1 5) = 1 + 10


(1 2)(1 5) = 11



Similarly, do the same for other elements.





Since,



Substituting the value of LHS,



We know by the property of matrices,



This implies,


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


Thus,


7 = 7


11 = 11


17 = k


23 = 23


Hence, k = 17.


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