Question

Last question on my test! Please help :)
Solve A = (-3, 2 ) over (1, 0 ) B = (-7, 6) over ( -6, -2)
determine the following: a) A X B b) 2A + 3B

Answer 1

Are these matrices? \[A = \left[\begin{matrix}-3 & 2 \\ 1 & 0\end{matrix}\right] ~\text{and}~ B =\left[\begin{matrix}-7 & 6 \\ -6 & -2\end{matrix}\right]\]

Answer 2

Correct.

Answer 3

Sorry for the delay. I was out to dinner.

To cross multiply matrices, we take the sum of the products of the columns of the first matrix and the rows of the second matrix. In this case, \[A \times B = \left[\begin{matrix}(-3*-7) + (2*-6) & (-3*6)+(2*-2) \\ (1*-7)+(0*-6) & (1*6)+(0*-2)\end{matrix}\right] = \left[\begin{matrix} 9 & -22 \\ -7 & 6 \end{matrix}\right]\]

To add matrices, we just add the numbers from the same index with each other. \[2A+3B = \left[\begin{matrix}2*-3+3*-7 & 2*2+3*6 \\ 2*1+3*-6 & 2*0+3*-2\end{matrix}\right] = \left[\begin{matrix}-27 & 22 \\ -16 & -6\end{matrix}\right]\]

Answer 4

Thanks so much!