Question

Perform the indicated matrix operations. If the matrix does not exist, write impossible47.$3\left[\begin{array}{cc}4& -2\\ -1& 7\end{array}\right]$

Short answer

The answer is$\left[\begin{array}{cc}12& -6\\ -3& 21\end{array}\right]$

Step-by-step solution

- State the definition of a matrix.

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

- 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:$3\left[\begin{array}{cc}4& -2\\ -1& 7\end{array}\right]$

Here, 3 is the scalar. Multiply each element of the matrix by 3.

$3\left[\begin{array}{cc}4& -2\\ -1& 7\end{array}\right]=\left[\begin{array}{cc}12& -6\\ -3& 21\end{array}\right]$

- State the conclusion.

Therefore, the resultant matrix is$\left[\begin{array}{cc}12& -6\\ -3& 21\end{array}\right]$