Question

Find the values of x and y in the following scalar multiplication.

Answer 1

Given:

`\begin{bmatrix}{1} & {0} & {x} \\ {y} & {-1} & {4} \\ {-3} & {5} & {1}\end{bmatrix}=\begin{bmatrix}{3} & {0} & {-9} \\ {6} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix}`

Find-: Value of "x" and "y"

Sol:

`\begin{gathered} =\begin{bmatrix}{1} & {0} & {x} \\ {y} & {-1} & {4} \\ {-3} & {5} & {1}\end{bmatrix} \\ \\ \text{ Multiply by 3 then:} \\ \\ =3*\begin{bmatrix}{1} & {0} & {x} \\ {y} & {-1} & {4} \\ {-3} & {5} & {1}\end{bmatrix} \\ \\ =\begin{bmatrix}{3} & {0} & {3x} \\ {3y} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix} \end{gathered}`

So, value of x and y is:

`\begin{bmatrix}{3} & {0} & {3x} \\ {3y} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix}=\begin{bmatrix}{3} & {0} & {-9} \\ {6} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix}`
`\begin{gathered} 3x=-9 \\ \\ x=-(9)/(3) \\ \\ x=-3 \\ \\ 3y=6 \\ \\ y=(6)/(3) \\ \\ y=2 \end{gathered}`

The value of "x" is -3 and value of "y" is 2.