Q6. - Algebra 2

Question

Perform the indicated matrix operations. 

$\left[\begin{array}{cc}3& 0\\ 7& 12\end{array}\right]-\left[\begin{array}{cc}6& -5\\ 4& -1\end{array}\right]$

Step-by-Step Solution

Answer

The answer is $\left[\begin{array}{cc}-3& 5\\ 3& 13\end{array}\right]$

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.

Matrices can be subtracted if they are of the same dimension.

 Here, both the matrices are of dimension $(2\times 2)$  that is both are of same dimension. Then subtraction can be performed.

 Subtract the corresponding elements

$\begin{array}{c}\left[\begin{array}{cc}3& 0\\ 7& 12\end{array}\right]-\left[\begin{array}{cc}6& -5\\ 4& -1\end{array}\right]=\left[\begin{array}{cc}3-6& 0-(-5)\\ 7-4& 12-(-1)\end{array}\right]\\ =\left[\begin{array}{cc}-3& 0+5\\ 3& 12+1\end{array}\right]\\ =\left[\begin{array}{cc}-3& 5\\ 3& 13\end{array}\right]\end{array}$

Step 3 - State the conclusion.

Therefore, the resultant matrix is $\left[\begin{array}{cc}-3& 5\\ 3& 13\end{array}\right]$