Problem

Given two matrices A and B, where A = \(\begin{bmatrix} 3 & 4 \\ 5 & 6 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\), find the result of the subtraction A - B.

Answer

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Answer

So, the result of the subtraction A - B is \(\begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix}\)

Steps

Step 1 :First, write the matrix A and B as follows: \(\begin{bmatrix} 3 & 4 \\ 5 & 6 \end{bmatrix} - \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\)

Step 2 :Then, subtract the elements in the same position in the two matrices to get the new matrix. The element at the first row and first column of the new matrix is the subtraction of the element at the first row and first column of matrix A and the element at the first row and first column of matrix B, which is 3 - 1 = 2. The element at the first row and second column of the new matrix is 4 - 2 = 2. The element at the second row and first column of the new matrix is 5 - 3 = 2. The element at the second row and second column of the new matrix is 6 - 4 = 2.

Step 3 :So, the result of the subtraction A - B is \(\begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix}\)

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