Question

Solve for x and y, if `2((1, 3),(0, x)) + ((y, 0),(1, 2)) = ((5, 6),(1, 8))`.

Answer 1

We have,

`2((1, 3),(0, x)) + ((y, 0),(1, 2)) = ((5, 6),(1, 8))`

Multiply the first matrix by 2,

`2((1, 3),(0, x)) = ((2, 6),(0, 2x))`

Add the two matrices,

`((2, 6),(0, 2x)) + ((y, 0),(1, 2)) = ((5, 6),(1, 8))`

= `((2 + y, 6),(1, 2x + 2)) = ((5, 6),(1, 8))`

On comparing, we get

2 + y = 5

y = 5 − 2

y = 3

2x + 2 = 8

2x = 8 − 2

2x = 6

x = `6/2`

x  = 3

Therefore x = 3 and y = 3