Question

Use matrices A, B, C, and D to find 4B-3D, if possible. If an operation is not defined, label it undefined.

Answer 1

We have to calculate the expression 4*B-3*D where B and D are matrices.

This can be performed because B and D have the same shape: they are 2-by-2 matrices.

We can then calculate the expression as:

`\begin{gathered} 4B-3D \\ 4\begin{bmatrix}{1} & {3} \\ {-2} & {4}\end{bmatrix}-3\begin{bmatrix}{5} & {-2} \\ {3} & {6}\end{bmatrix} \\ \begin{bmatrix}{4} & {12} \\ {-8} & {16}\end{bmatrix}-\begin{bmatrix}{15} & {-6} \\ {9} & {18}\end{bmatrix} \\ \begin{bmatrix}{4-15} & {12-(-6)} \\ {-8-9} & {16-18}\end{bmatrix} \\ \begin{bmatrix}{-11} & {18} \\ {-17} & {-2}\end{bmatrix} \end{gathered}`

Answer: the result is [-11, 18; -17, -2]