Q15. - Algebra 1

Question

Perform the indicated matrix operations. If an operation cannot be performed, write impossible.

$\mathbf{\left[}\begin{array}{ccc}\mathbf{3}& \mathbf{-}\mathbf{5}& \mathbf{2}\end{array}\mathbf{\right]}\mathbf{+}\mathbf{\left[}\begin{array}{ccc}\mathbf{12}& \mathbf{-}\mathbf{7}& \mathbf{-}\mathbf{6}\end{array}\mathbf{\right]}$

Step-by-Step Solution

Answer

The result after performing the indicated matrix operations is $\mathbf{\left[}\begin{array}{ccc}\mathbf{15}& \mathbf{-}\mathbf{12}& \mathbf{-}\mathbf{4}\end{array}\mathbf{\right]}$.

Step 1. Write the condition for the addition of two matrices.

The two matrices $A$ and $B$ can be added if both matrices $A$ and $B$ have same order.

The matrix obtained after the addition of the two matrices has the same order as that of the matrices which are added and the matrix after the addition can be obtained by adding the corresponding elements of the two matrices.

Step 2. Add the given matrices.

The order of the matrix $\left[\begin{array}{ccc}3& -5& 2\end{array}\right]$ is $1\times 3$.

The order of the matrix $\left[\begin{array}{ccc}12& -7& -6\end{array}\right]$ is $1\times 3$.

As, the order of the matrices is same. Therefore, the given matrices can be added and the addition of two matrices can be obtained by adding the corresponding elements of the given matrices.

The result after the addition of the given matrices is:

$\begin{array}{r}\left[\begin{array}{ccc}3& -5& 2\end{array}\right]+\left[\begin{array}{ccc}12& -7& -6\end{array}\right]=[\begin{array}{ccc}3+12& -5+(-7)& 2\end{array}+(-6)]\\ =\left[\begin{array}{crc}3+12& -5-7& 2-6\end{array}\right]\\ =\left[\begin{array}{ccc}15& -12& -4\end{array}\right]\end{array}$

Therefore, the result after performing the indicated matrix operations is $\left[\begin{array}{ccc}15& -12& -4\end{array}\right]$.