Question

Perform the indicated matrix operations:
\(\begin{bmatrix}5 & 4 \\-3 & 7 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix}-4 & 8 \\6 & 0 \\ -5 & 3 \end{bmatrix}\)

Answer 1

Step 1
According to he question,, we have to subtract the given two matrix \(\begin{bmatrix}5 & 4 \\-3 & 7 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix}-4 & 8 \\6 & 0 \\ -5 & 3 \end{bmatrix}\) .
Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.
We can perform the operations like addition or subtraction with the corresponding elements and solve accordingly.
Step 2
Rewrite the given matrices,
\(\begin{bmatrix}5 & 4 \\-3 & 7 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix}-4 & 8 \\6 & 0 \\ -5 & 3 \end{bmatrix}\)
Now subtract the corresponding elements,so,
\(\begin{bmatrix}5 & 4 \\-3 & 7 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix}-4 & 8 \\6 & 0 \\ -5 & 3 \end{bmatrix}=\begin{bmatrix}5+4 & 4-8 \\-3-6 & 7-0 \\ 0+5 & 1-3 \end{bmatrix}\)
\(=\begin{bmatrix}9 & -4 \\-9 & 7 \\ 5 & -2 \end{bmatrix}\)
Hence, the value of the matrices \(\begin{bmatrix}5 & 4 \\-3 & 7 \\ 0 & 1 \end{bmatrix}-\begin{bmatrix}-4 & 8 \\6 & 0 \\ -5 & 3 \end{bmatrix}\) is \(\begin{bmatrix}9 & -4 \\-9 & 7 \\ 5 & -2 \end{bmatrix}\)