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Let [tex]$A=\left[\begin{array}{rr}-5 & 1 \\ 4 & 0\end{array}\right]$[/tex] and [tex]$B=\left[\begin{array}{rr}-1 & -2 \\ 6 & 6\end{array}\right]$[/tex].

Find [tex][tex]$B-A$[/tex][/tex], if possible.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. [tex]$B - A =$ \begin{bmatrix} \square & \square \\ \square & \square \end{bmatrix}[/tex]
(Type an integer or simplified fraction for each matrix element.)

B. [tex]$B-A$[/tex] is undefined.

Sagot :

GinnyAnsweridn
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]
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