Question

Evaluate

Answer 1

multiplying a 3 by 2 with a 2 by 3
will result in a 3 by 3
the inner numbers have to match
then the dimensions of the product will be the exterior numbers there

Answer 2

wait, what do you mean 3 by 2 and 2 by 3?

Answer 3

those are the dimensions of your matrices respectively

Answer 4

anyways to find the entries you do rows from the first matrix with columns of the second matrix

Answer 5

for example
entry 1 will be 2(5)+0(0)

Answer 6

in general the first element in the product matrix would look like this
\[\left[\begin{matrix}a_{11} & a_{12} \\ a_{21} & a_{22} \\ a_{31} & a_{32}\end{matrix}\right] \cdot \left[\begin{matrix}b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23}\end{matrix}\right] \\ =\left[\begin{matrix}a_{11} \cdot b_{11}+a_{12} \cdot b_{21} & ? & ? \\ ? & ? & ? \\ ? & ? & ?\end{matrix}\right]\]

Answer 7

basically we did the dot product of <a11,a12> and <b11,b21>

Answer 8

to find the first entry that is