To find the matrix [tex]\( B - A \)[/tex], we need to perform subtraction of the corresponding elements from matrix [tex]\( A \)[/tex] and matrix [tex]\( B \)[/tex].
Given matrices:
[tex]\[ A = \begin{pmatrix} -5 & 1 \\ 4 & 0 \end{pmatrix} \][/tex]
[tex]\[ B = \begin{pmatrix} -1 & -2 \\ 6 & 6 \end{pmatrix} \][/tex]
The subtraction [tex]\( B - A \)[/tex] is performed element-wise as follows:
For the first element in the first row and first column:
[tex]\[ -1 - (-5) = -1 + 5 = 4 \][/tex]
For the second element in the first row and second column:
[tex]\[ -2 - 1 = -2 - 1 = -3 \][/tex]
For the first element in the second row and first column:
[tex]\[ 6 - 4 = 2 \][/tex]
For the second element in the second row and second column:
[tex]\[ 6 - 0 = 6 \][/tex]
Putting it all together, we get:
[tex]\[ B - A = \begin{pmatrix} 4 & -3 \\ 2 & 6 \end{pmatrix} \][/tex]
So the correct choice is:
A. [tex]\( B - A = \begin{pmatrix} 4 & -3 \\ 2 & 6 \end{pmatrix} \)[/tex]
