Question

Please help thank you If A = [[1,5] [-3,4]] and B = [[2,6] [6.-1]], find AB.

Answer 1

`AB=\left[\begin{array}{cc}32&1&18&-22\\\end{array}\right]`

Explanation:

To multiply matrices, we need to take the dot product of each row and column.

First, the dot product of (1,5) and (2,6) is what goes in the top-leftmost section of the resulting matrix. So the dot product would be (1*2)+(5*6)=2+30=32.

Second, the dot product of (1,5) and (6,-1) is what goes in the top-rightmost section of the resulting matrix. So the dot product would be (1*6)+(5*-1)=6-5=1.

Third, the dot product of (-3,4) and (2,6) is what goes in the bottom-leftmost section of the resulting matrix. So the dot product would be (-3*2)+(4*6)=-6+24=18.

Fourth, the dot product of (-3,4) and (6,-1) is what goes in the bottom-rightmost section of the resulting matrix. So the dot product would be (-3*6)+(4*-1)=-18-4=-22.

Therefore, the resulting matrix is
`\left[\begin{array}{cc}32&1&18&-22\\\end{array}\right]`