Question

Determine whether the product is defined or undefined. If defined, give the dimensions of the product matrix.

Answer 1

There is a nice little thing that if you multiply an i x j matrix by a j x k matrix then the matrix you get out is an i x k matrix. So just make sure that the columns of the first matrix match the number of rows in the second matrix.

\[A_{ij}B{jk}=C_{ik}\]

Answer 2

=\left[\begin{matrix}(1)(9)+(1)(1)+(-4)(-7)\\(5)(9)+(6)(1)+(0)(-7)
\end{matrix}\right]

Answer 3

okay so that turned out weird but is that how i would do it?

Answer 4

That looks right to me =)

Answer 5

then do you just add them?

Answer 6

Yeah, just normal algebra inside there, you'll get something that looks like this: \[\left[\begin{matrix}? \\?\end{matrix}\right]\]

Answer 7

\[\left(\begin{matrix}38 \\ 51\end{matrix}\right)\]

Answer 8

so the dimensions would be 2x1