Finding Variables within Matricies Question

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Discussion Overview

The discussion revolves around finding the variable \( k \) in a matrix multiplication problem involving three matrices. Participants are exploring the multiplication of a horizontal matrix, a 2x2 matrix, and a vertical matrix, leading to a scalar result of 11. The focus is on the mathematical reasoning and steps involved in this process.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the multiplication of the matrices and the resulting expression for the vertical matrix.
  • Another participant suggests re-evaluating the multiplication to confirm that the result should be a scalar (1x1 matrix).
  • A third participant clarifies the multiplication steps and confirms that the product will yield a quadratic equation for \( k \).
  • A later reply acknowledges the clarification and expresses gratitude for the assistance.

Areas of Agreement / Disagreement

Participants generally agree on the steps needed to multiply the matrices and the expectation of obtaining a quadratic equation, but the initial confusion about the multiplication process indicates some uncertainty.

Contextual Notes

There may be limitations in the understanding of matrix multiplication rules or the specific arrangement of the matrices that could affect the clarity of the problem.

Emma O'shea
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:confused: 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
 
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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.
 
Just for reference, is the product
[tex]\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[/tex]?

If so, as matt grime says, go ahead and multiply it out. The first product
[tex]\left(\begin{array}{cc}3 & 4 \\ -2 & 1\end{array}\right)\left(\begin{array}{c}1 \\ k\end{array}\right)[/tex]
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.
 
Hi

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

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