Question

Given the matrices A and B shown below, find – į A+ B.89A=12 4.-4 -10-6 12B.=-3-19-10

Answer 1

Given:

`\begin{gathered} A=\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ B=\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \end{gathered}`

Now, let's find (-1/2)A.

Each term of the matrix A is multiplied by -1/2.

`\begin{gathered} (-1)/(2)A=(-1)/(2)\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ =\begin{bmatrix}{(-12)/(2)} & {(-4)/(2)} & {} \\ {(4)/(2)} & {(10)/(2)} & {} \\ {(6)/(2)} & {-(12)/(2)} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix} \end{gathered}`

Now let's find (-1/2)A+B.

To find (-1/2)A+B, the corresponding terms of the matrices are added together.

`\begin{gathered} (-1)/(2)A+B=\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix}+\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6+8} & {-2+9} & {} \\ {2-3} & {5-1} & {} \\ {3-9} & {-6-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{2} & {7} & {} \\ {-1} & {4} & {} \\ {-6} & {-16} & {}\end{bmatrix} \end{gathered}`

Therefore,