Finding Variables within Matricies Question

[Emma O'shea]

Hi There!
I have a quick question and I would really appreciate some guidence!

I have three matrix multiplied together like so

(horizontal matrix 1 k)(2x2 matrix 3 4 -2 1)(vertical matrix 1 k) equals 11

I'm asked to find two values for k.
I've tried multiplying them out but i end up with something like the vertical matrix 3-2k 4k+k^2 equals 11. Not sure what to do from there... Any ideas
!
Thanks for your replies

 

[matt grime]

Try mulitplying them out again: you should have a 1x1 matrix at the end (ie a scalar): you are multiplying 1x2, 2x2, 2x1 matrices, so the answer is 1x1.

 

[HallsofIvy]

Just for reference, is the product
$$\left(\begin{array}{cc}1&k\end{array}\right)\left(\begin{array}{cc}3 & 4 \\ -2 & 1\end{array}\right)\left(\begin{array}{c}1 \\ k\end{array}\right)= 11$$?

If so, as matt grime says, go ahead and multiply it out. The first product
$$\left(\begin{array}{cc}3 & 4 \\ -2 & 1\end{array}\right)\left(\begin{array}{c}1 \\ k\end{array}\right)$$
will be a vertical 1x2 matrix and then the product of horizontal and vertical matrices is a number (technically, a 1 by 1 matrix).
You will get a quadratic equation for k.

 

[Emma O'shea]

Hi

Ya that's the one!
Thanks guys!
Much appreciated!