Question

Solve the matrix equation `((x^2),(y^2)) - 3((x),(2y)) = ((-2),(-9))`.

Answer 1

`((x^2),(y^2)) - 3((x),(2y)) = ((-2),(-9))`

Multiply the second matrix by 3,

`3((x),(2y))

= ((3x),(6y))`

Subtract the matrices,

`((x^2),(y^2)) - ((3x),(6y))`

= `((x^2 - 3x),(y^2 - 6y))`

`((x^2 - 3x),(y^2 - 6y)) = ((-2),(-9))`

Equate corresponding elements,

x² − 3x = −2

x² − 3x + 2 = 0

(x − 1) (x − 2) = 0

x = 1 or x = 2

y² − 6y = −9

(y − 3)² = 0

y = 3