To find the matrix \( B - A \), we first need to subtract the corresponding elements of matrix \( A \) from matrix \( B \). Given the matrices:
\[ A = \begin{bmatrix} -3 & 5 & 0 & 2 \ -3 & 4 & 0 & 0 \end{bmatrix} \]
\[ B = \begin{bmatrix} -5 & -2 & 5 & -5 \ 4 & -5 & -2 & -1 \end{bmatrix} \]
We'll perform the element-wise subtraction for each position in the matrices.
Calculation
For the first row:
- First column: \( -5 - (-3) = -5 + 3 = -2 \)
- Second column: \( -2 - 5 = -7 \)
- Third column: \( 5 - 0 = 5 \)
- Fourth column: \( -5 - 2 = -7 \)
For the second row:
- First column: \( 4 - (-3) = 4 + 3 = 7 \)
- Second column: \( -5 - 4 = -9 \)
- Third column: \( -2 - 0 = -2 \)
- Fourth column: \( -1 - 0 = -1 \)
Putting it all together
Now, we can write the result of \( B - A \):
\[ B - A = \begin{bmatrix} -2 & -7 & 5 & -7 \ 7 & -9 & -2 & -1 \end{bmatrix} \]
Thus, the final result is:
\[ B - A = \begin{bmatrix} -2 & -7 & 5 & -7 \ 7 & -9 & -2 & -1 \end{bmatrix} \]