Question

Given these matrices, how are each variable (x,y,z) translated? I'm stuck!

Answer 1

`2A+B=\begin{bmatrix}{5} & {2} & {3} \\ {9} & {0} & {1} \\ {7} & {6} & {-1}\end{bmatrix}`

Let's solve for B:

`\begin{gathered} \text{Subtract 2A from both sides:} \\ 2A+B-2A=\begin{bmatrix}{5} & {2} & {3} \\ {9} & {0} & {1} \\ {7} & {6} & {-1}\end{bmatrix}-2A \\ \\ B=\begin{bmatrix}{5} & {2} & {3} \\ {9} & {0} & {1} \\ {7} & {6} & {-1}\end{bmatrix}-2\begin{bmatrix}{1} & {2} & {1} \\ {3} & {1} & {0} \\ {2} & {4} & {-1}\end{bmatrix} \\ \\ B=\begin{bmatrix}{5} & {2} & {3} \\ {9} & {0} & {1} \\ {7} & {6} & {-1}\end{bmatrix}-\begin{bmatrix}{2} & {4} & {2} \\ {6} & {2} & {0} \\ {4} & {8} & {-2}\end{bmatrix} \end{gathered}`

Therefore:

`\begin{gathered} B=\begin{bmatrix}{5-2} & {2-4} & {3-2} \\ {9-6} & {0-2} & {1-0} \\ {7-4} & {6-8} & {-1-(-2)}\end{bmatrix} \\ \\ B=\begin{bmatrix}{3} & {-2} & {1} \\ {3} & {-2} & {1} \\ {3} & {-2} & {1}\end{bmatrix} \end{gathered}`