Q20. - Algebra 2

Question

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

 

$\left[\begin{array}{cc}1.35& 5.80\\ 1.24& 14.32\\ 6.10& 35.26\end{array}\right]+\left[\begin{array}{cc}0.45& 3.28\\ 1.94& 16.72\\ 4.31& 21.30\end{array}\right]$

Step-by-Step Solution

Answer

The final matrix after performing the indicated matrix operations is

$\left[\begin{array}{cc}1.35& 5.80\\ 1.24& 14.32\\ 6.10& 35.26\end{array}\right]+\left[\begin{array}{cc}0.45& 3.28\\ 1.94& 16.72\\ 4.31& 21.30\end{array}\right]=\left[\begin{array}{cc}\text{1.8}& \text{9.08}\\ \text{3.18}& \text{31.04}\\ \text{10.41}& \text{56.56}\end{array}\right]$.

Step 1 - Define concept of matrix addition

If A and B are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order $m\times n$ wherein each element is the sum of the corresponding elements.

Step 2 - Add corresponding elements

In order to find $\left[\begin{array}{cc}1.35& 5.80\\ 1.24& 14.32\\ 6.10& 35.26\end{array}\right]+\left[\begin{array}{cc}0.45& 3.28\\ 1.94& 16.72\\ 4.31& 21.30\end{array}\right]$, add corresponding elements of both the matrices.

$\left[\begin{array}{cc}1.35& 5.80\\ 1.24& 14.32\\ 6.10& 35.26\end{array}\right]+\left[\begin{array}{cc}0.45& 3.28\\ 1.94& 16.72\\ 4.31& 21.30\end{array}\right]=\left[\begin{array}{cc}1.35+0.45& 5.80+3.28\\ 1.24+1.94& 14.32+16.72\\ 6.10+4.31& 35.26+21.30\end{array}\right]$

Step 3 - Simplify the matrix

Further simplify the matrix by adding the elements.

 

 $\begin{array}{c}\left[\begin{array}{cc}1.35& 5.80\\ 1.24& 14.32\\ 6.10& 35.26\end{array}\right]+\left[\begin{array}{cc}0.45& 3.28\\ 1.94& 16.72\\ 4.31& 21.30\end{array}\right]=\left[\begin{array}{cc}1.35+0.45& 5.80+3.28\\ 1.24+1.94& 14.32+16.72\\ 6.10+4.31& 35.26+21.30\end{array}\right]\\ =\left[\begin{array}{cc}\text{1.8}& \text{9.08}\\ \text{3.18}& \text{31.04}\\ \text{10.41}& \text{56.56}\end{array}\right]\end{array}$