To subtract the given matrices, we perform element-wise subtraction between the corresponding elements of the two matrices. Let's go through this step-by-step:
Given matrices:
[tex]\[
A = \begin{bmatrix}
5 & -1 \\
2 & 4
\end{bmatrix}
\][/tex]
[tex]\[
B = \begin{bmatrix}
2 & 6 \\
-3 & -4
\end{bmatrix}
\][/tex]
We need to find the matrix [tex]\( C = A - B \)[/tex].
To do that, subtract each element of matrix [tex]\( B \)[/tex] from the corresponding element of matrix [tex]\( A \)[/tex]:
1. Top-left element:
[tex]\[
c_{11} = a_{11} - b_{11} = 5 - 2 = 3
\][/tex]
2. Top-right element:
[tex]\[
c_{12} = a_{12} - b_{12} = -1 - 6 = -7
\][/tex]
3. Bottom-left element:
[tex]\[
c_{21} = a_{21} - b_{21} = 2 - (-3) = 2 + 3 = 5
\][/tex]
4. Bottom-right element:
[tex]\[
c_{22} = a_{22} - b_{22} = 4 - (-4) = 4 + 4 = 8
\][/tex]
Combining these results, we get the resulting matrix [tex]\( C \)[/tex]:
[tex]\[
C = \begin{bmatrix}
3 & -7 \\
5 & 8
\end{bmatrix}
\][/tex]
Therefore, the resulting matrix after subtracting matrix [tex]\( B \)[/tex] from matrix [tex]\( A \)[/tex] is:
[tex]\[
\begin{bmatrix}
3 & -7 \\
5 & 8
\end{bmatrix}
\][/tex]
