Matrix Question.

[thesloc]

Hello and thanks for ANY hint/help.

I have this problem....

What matrix must you multiply by
|5 31|
|1 2 0|

to get

|1 .6 .2|
|-.5 -1 0|
?

Any help is much appreciated. Thanks.[/code]

 

[stapel]

Looking at the dimensions, and naming the first matrix "A", the last matrix "C", and the unknown matrix "B", and assuming that you mean to find B such that AB = C, then you can see that you need a 3-by-3 matrix for B.

But if you look at the relative changes in the row values between A and C, it should be pretty easy to come up with the entries of B. Hint: Most of the entries will be zeroes.

Eliz.

 

[soroban]

Hello, thesloc!

Where did this question come from?
Is there more to the problem? .There is an infinitude of soltutions.

What matrix must you multiply by \(\displaystyle \left|\begin{array}{cc}5\, & 3\, & 1 \\ 1\, & 2\, & 0\end{array}\right|\) to get: \(\displaystyle \left|\begin{array}{ccc}0\, & 0.6\, & 0.2\\ \\ -0.5\, & -1\, & 0\end{array}\right|\)

Since \(\displaystyle [2\times3]\cdot[3\times3]\:=\:[2\times3]\), we want a \(\displaystyle 3\times3\) matrix . . . as Eliz pointed out.

Since it has 9 elements and we have at most 6 equations, the solution is not unique.

Here is my solution: . \(\displaystyle \left|\begin{array}{ccccccc}a & b & c \\ \: & \: & . \\-\frac{1}{4}(2a+1) & -\frac{1}{2}(b+1) & -\frac{1}{2}c \\ \, & . & \,\\-\frac{7}{4}(2a-1) & -\frac{7}{10}(5b-3) & -\frac{1}{10}(35c-2)\end{array}\right|\)