Find the values of x and y, if 2[(1,3)(0,x)] + [(y,0)(1,2)] = [(5,6)(1,8)].

Question

Find the values of x and y, if

\(2 \begin{bmatrix} 1 &3 \\[0.3em] 0& \text{x} \\[0.3em] \end{bmatrix}\) + \( \begin{bmatrix} y& 0 \\[0.3em] 1 & 2 \\[0.3em] \end{bmatrix}\) = \( \begin{bmatrix} 5& 6 \\[0.3em] 1 & 8 \\[0.3em] \end{bmatrix}.\) 

2[(1,3)(0,x)] + [(y,0)(1,2)] = [(5,6)(1,8)].

Answer 1

Given,

Using the property of matrix multiplication such that h is scalar,

Using the matrix property of matrix addition, when two matrices are of the same order then, 

each element gets added to the corresponding element,

Comparing each element we get,

2 + y = 5, ⇒ y = 3

2x + 2 = 8, ⇒ x = 3