Question

Evaluate the expression

Answer 1

Evaluating the expression
`6(\left[\begin{array}{ccc}-3&0&1\\0&3&5\end{array}\right] - \left[\begin{array}{ccc}4&1&-2\\3&-9&0\end{array}\right] )` results in
`\left[\begin{array}{ccc}-42&-6&18\\-18&72&30\end{array}\right]`.

Generally, matrice operations involve three algebraic operations, including the addition of matrices, subtraction of matrices, and multiplication of matrices.

First Matrix - Second Matrix = ((-3 - 4) (0 - 1) (1 - (-2)) (0 - 3) (3 - (-9)) (5 - 0)) =

`\left[\begin{array}{ccc}-7&-1&3\\-3&12&5\end{array}\right]`

Now, we multiply the result by 6: 6 *
`\left[\begin{array}{ccc}-7&-1&3\\-3&12&5\end{array}\right]` =
`\left[\begin{array}{ccc}-42&-6&18\\-18&72&30\end{array}\right]`

Thus, the final result after subtracting the second matrix from the first matrix and multiplying by 6 is
`\left[\begin{array}{ccc}-42&-6&18\\-18&72&30\end{array}\right]`.