Given two 2x2 matrices A = \( \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) and B = \( \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \), what is the result of A - B?
Answer
So, \( A - B = \begin{bmatrix} -4 & -4 \\ -4 & -4 \end{bmatrix} \)
Step 1 ：First, set up the subtraction. \( A - B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} - \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \)
Step 2 ：Subtract the corresponding elements in the matrices. The element in the first row and first column of the result is \(1 - 5 = -4\). The element in the first row and second column is \(2 - 6 = -4\). The element in the second row and first column is \(3 - 7 = -4\). The element in the second row and second column is \(4 - 8 = -4\).
Step 3 ：So, \( A - B = \begin{bmatrix} -4 & -4 \\ -4 & -4 \end{bmatrix} \)
