Question

Watch help videoGiven the matrices A and B shown below, find – B - A.318154B12be-12

Answer 1

Given two matrices

`A=\begin{bmatrix}{-18} & {3} & {} \\ {-15} & {-6} & {} \\ {} & {} & {}\end{bmatrix},B=\begin{bmatrix}{-4} & {12} & {} \\ {8} & {-12} & {} \\ {} & {} & {}\end{bmatrix}`

We will solve for the resultant matrix -B - 1/2A.

This operation is represented as

`-B-(1)/(2)A=-\begin{bmatrix}{-4} & {12} & {} \\ {8} & {-12} & {} \\ {} & {} & {}\end{bmatrix}-(1)/(2)\begin{bmatrix}{-18} & {3} & {} \\ {-15} & {-6} & {} \\ {} & {} & {}\end{bmatrix}`

Let's simplify the matrices further based on scalar operations that can be done here. The B matrix will be multiplied by -1 while the A matrix will be multiplied by 1/2. We now have

`-B-(1)/(2)A=\begin{bmatrix}{4} & {-12} & {} \\ {-8} & {12} & {} \\ {} & {} & {}\end{bmatrix}-\begin{bmatrix}{-9} & {(3)/(2)} & {} \\ {(-15)/(2)} & {-3} & {} \\ {} & {} & {}\end{bmatrix}`

Now, we apply the subtraction of matrices to the simplified matrix operation above. We have

`\begin{gathered} -B-(1)/(2)A=\begin{bmatrix}{4-(-9)} & {-12-(3)/(2)} & {} \\ {-8-(-(15)/(2))} & {12-(-3)} & {} \\ {} & {} & {}\end{bmatrix} \\ -B-(1)/(2)A=\begin{bmatrix}{4+9} & {-12-(3)/(2)} & {} \\ {-8+(15)/(2)} & {12+3} & {} \\ {} & {} & {}\end{bmatrix} \\ -B-(1)/(2)A=\begin{bmatrix}{13} & {(-27)/(2)} & {} \\ {-(1)/(2)} & {15} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}`

Hence, the resulting matrix for the operation -B - 1/2A is

`-B-(1)/(2)A=\begin{bmatrix}{13} & {(-27)/(2)} & {} \\ {-(1)/(2)} & {15} & {} \\ {} & {} & {}\end{bmatrix}`