Find the value of x and y for which [(x,y)(3y,x)] [(1,2)] = [(3,5)]

Question

Find the value of x and y for which

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

[(x,y)(3y,x)] [(1,2)] = [(3,5)]

Answer 1

Given,

Applying matrix multiplication we have,

On comparing the elements with each other we get,

The linear equations, x + 2y = 3, 3y + 2x = 5

On solving these equations we get x = 1, y = 1