Given matrices A = ( begin{bmatrix} 2 & 3 4 & -1 end{bmatrix} ) and B = ( begin{bmatrix} 1 & 2 3 & 1 end{bmatrix} ), compute the product AB.

Question

Given matrices A = ( begin{bmatrix} 2 & 3  4 & -1  end{bmatrix} ) and B = ( begin{bmatrix} 1 & 2  3 & 1  end{bmatrix} ), compute the product AB.

Accepted Answer

Step:1 ：Multiply the first row of A by the first column of B: ( (2*1) + (3*3) = 2 + 9 = 11 )Step:2 ：Multiply the first row of A by the second column of B: ( (2*2) + (3*1) = 4 + 3 = 7 )Step:3 ：Multiply the second row of A by the first column of B: ( (4*1) + (-1*3) = 4 - 3 = 1 )Step:4 ：Multiply the second row of A by the second column of B: ( (4*2) + (-1*1) = 8 - 1 = 7 )Step:5 ：The resulting matrix is therefore ( begin{bmatrix} 11 & 7  1 & 7  end{bmatrix} )

Answer

Step: 1 ：Multiply the first row of A by the first column of B: ( (2*1) + (3*3) = 2 + 9 = 11 )Step: 2 ：Multiply the first row of A by the second column of B: ( (2*2) + (3*1) = 4 + 3 = 7 )Step: 3 ：Multiply the second row of A by the first column of B: ( (4*1) + (-1*3) = 4 - 3 = 1 )Step: 4 ：Multiply the second row of A by the second column of B: ( (4*2) + (-1*1) = 8 - 1 = 7 )Step: 5 ：The resulting matrix is therefore ( begin{bmatrix} 11 & 7  1 & 7  end{bmatrix} )

Given matrices A = \( \begin{bmatrix} 2 & 3 \\ 4 & -1 \\ \end{bmatrix} \) and B = \( \begin{bmatrix} 1 & 2 \\ 3 & 1 \\ \end{bmatrix} \), compute the product AB.

Answer

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