Question

Match the lettered entries to the matrices a, b, and ab.

Answer 1

`\begin{gathered} A=\begin{bmatrix}{a} & {2} & {3} \\ 4{} & {b} & {6} \\ {c} & {8} & {-7}\end{bmatrix} \\ B=\begin{bmatrix}{5} & {1} & {-2} \\ {-1} & {3} & {4} \\ {2} & {d} & {e}\end{bmatrix} \\ AB_(11)=5a+4=14 \\ AB_(12)=a+6+3d=-1 \\ AB_(13)=-2a+8+3e=f \\ AB_(21)=32-b=20 \\ AB_(22)=4+3b+6d=22 \\ AB_(23)=-8+4b+6e=70 \\ AB_(31)=5c-22=-27 \\ AB_(32)=c+24-7d=44 \\ AB_(33)=-2c+32-7e=-1 \\ a=(14-4)/(5)=2 \\ d=(-1-6-2)/(3)=-3 \\ b=32-20=12 \\ e=(70+8-4\cdot12)/(6)=5 \\ f=-2\cdot2+8+3\cdot5=19 \\ c=(-27+22)/(5)=-1 \end{gathered}`