Question

Find the difference of the matrices. $$ \left[\begin{array}{rr} -4 & 1 \\ 0 & -13 \\ 2 & -8 \end{array}\right]-\left[\begin{array}{rr} -6 & 3 \\ -5 & 8 \\ 2 & -7 \end{array}\right] $$

Short answer

The difference between the two given matrices is:\[\left[\begin{array}{rr} 2 & -2 \ 5 & -21 \ 0 & -1\end{array}\right]\]

Step-by-step solution

Identify Corresponding Elements

First, identify the elements that are in the same position in both matrices for subtraction. The matrices have the same sizes, so all corresponding element positions in the two matrices are the same.

Subtract Corresponding Elements

Next, Subtract each element in the second matrix from the corresponding element in the first matrix. This will give your difference matrix: \[\left[\begin{array}{rr} -4-(-6) & 1-3 \ 0-(-5) & -13-8 \ 2-2 & -8-(-7)\end{array}\right]\]

Calculation of Each Element

Finally, perform the subtraction for each element. This will give the final difference between the two matrices: \[\left[\begin{array}{rr} 2 & -2 \ 5 & -21 \ 0 & -1\end{array}\right]\]