Q8. - Algebra 2

Question

Perform the indicated matrix operations.8.

$5\left[\begin{array}{l}\begin{array}{ccc}-2& 4& 5\end{array}\\ \begin{array}{ccc}0& -4& 7\end{array}\end{array}\right]$

Step-by-Step Solution

Answer

The answer is $\left[\begin{array}{ccc}-10& 20& 25\\ 0& -20& 35\end{array}\right]$

Step 1 - State the definition of a matrix.

A rectangular array of numbers arranged in rows and columns is called a matrix.

Step 2 - Solve the matrix.

To evaluate the matrix use scalar multiplication. 

 Scalar multiplication is the method in which matrix is multiplied by a constant called scalar.

 The matrix is:$5\left[\begin{array}{ccc}-2& 4& 5\\ 0& -4& 7\end{array}\right]$

Here, 5 is the scalar. Multiply each element of the matrix by 5.

$\begin{array}{c}5\left[\begin{array}{ccc}-2& 4& 5\\ 0& -4& 7\end{array}\right]=\left[\begin{array}{ccc}5\times -2& 5\times 4& 5\times 5\\ 5\times 0& 5\times -4& 5\times 7\end{array}\right]\\ =\left[\begin{array}{ccc}-10& 20& 25\\ 0& -20& 35\end{array}\right]\end{array}$

Step 3 - State the conclusion.

Therefore, the resultant matrix is $\left[\begin{array}{ccc}-10& 20& 25\\ 0& -20& 35\end{array}\right]$