Chapter 12.5, Problem 1MCQ

To determine

To find: The sum of two matrices $\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]+\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]$ .

Answer to Problem 1MCQ

The sum of two matrices is $\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]+\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]=\left[\begin{array}{c}2\\ 3\\ -4\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}2\\ 4\\ 3\end{array}\right]$ .

Explanation of Solution

Given information:

The given expression is

  $\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]+\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]$ .

Calculation:

Consider the expression

The two matrices;

  $\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]+\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]\mathrm{..........}\left(1\right)$

To find the sum of two matrices given in $\left(1\right)$ , let us consider

  $A=\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]$ , and $B=\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]$

Before adding these matrices, first we check the size of both matrices if both the matrices have same size, then addition is possible.

Here matrix $A$ has $3$ rows and $2$ columns, and matrix $B$ is has $3$ rows and $2$ .columns, therefore we can say both the matrix have same size. Then we have to add corresponding elements of these two matrices.

  $A+B=\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]+\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]$

  $=\left[\begin{array}{c}-2+4\\ 0+3\\ -1+\left(-3\right)\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3+\left(-1\right)\\ 4+0\\ 1+2\end{array}\right]$ Adding corresponding elements

  $=\left[\begin{array}{c}2\\ 3\\ -4\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}2\\ 4\\ 3\end{array}\right]$ Simplify.

Therefore the sum of two matrices is $\left[\begin{array}{c}-2\\ 0\\ -1\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}3\\ 4\\ 1\end{array}\right]+\left[\begin{array}{c}4\\ 3\\ -3\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}-1\\ 0\\ 2\end{array}\right]=\left[\begin{array}{c}2\\ 3\\ -4\end{array}\begin{array}{c}\\ \\ \end{array}\begin{array}{c}2\\ 4\\ 3\end{array}\right]$ .