## Can somebody help with this matrix problem?

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littlebu
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### Can somebody help with this matrix problem?

I am sure that this is an easy one, but I don't know where to start. I'm taking an online course and all the examples in the book are nothing like this one. Here's the question:

Find the matrix A such that

A
• [1 0] = [-5 -4]
[-1 4] [7 12]
Hint: Let A =
• [a b]
[c d]

not looking for the answer just an explanation on where to start. Thanks

stapel_eliz
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Find the matrix A such that

A
• [1 0] = [-5 -4]
[-1 4] [7 12]
Is the "A"off to one side meant to indicate multiplication, so the exercise is as follows?
$\mbox{Find the matrix }\, A\, \mbox{such that}$

. . . . .$A\,\times\,\left[\begin{array}{rr}1&0\\-1&4\end{array}\right]\, =\, \left[\begin{array}{rr}-5&-4\\7&12\end{array}\right]$
If so, have you tried using the hint? (If yes, please reply showing your work so far.)

Also, have you yet learned about finding inverse matrices?

Thank you!

Martingale
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### Re:

Find the matrix A such that

A
• [1 0] = [-5 -4]
[-1 4] [7 12]
Is the "A"off to one side meant to indicate multiplication, so the exercise is as follows?
$\mbox{Find the matrix }\, A\, \mbox{such that}$

. . . . .$A\,\times\,\left[\begin{array}{rr}1&0\\-1&4\end{array}\right]\, =\, \left[\begin{array}{rr}-5&-4\\7&12\end{array}\right]$
If so, have you tried using the hint? (If yes, please reply showing your work so far.)

Also, have you yet learned about finding inverse matrices?

Thank you!
based on the hint I would bet not.

the original poster is probably required to multiply out the left hand side then set up a system of 4 equations an 4 unknowns and solve this system for a,b,c,d.
Last edited by Martingale on Mon Dec 06, 2010 11:45 pm, edited 1 time in total.

littlebu
Posts: 8
Joined: Fri Oct 22, 2010 9:23 pm
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### Re:

Is the "A"off to one side meant to indicate multiplication, so the exercise is as follows?
$\mbox{Find the matrix }\, A\, \mbox{such that}$

. . . . .$A\,\times\,\left[\begin{array}{rr}1&0\\-1&4\end{array}\right]\, =\, \left[\begin{array}{rr}-5&-4\\7&12\end{array}\right]$
Yes the problem is written as A[....]

The problem I am having is were to start. I know that AX=B so I'm simply solving for A. Sigh I knew I was over thinking it. When I solve it I will post my solution to ensure I did the problem properly.

littlebu
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### Re: Re:

So not as simple as I thought or is it?

Since AX=B

[a b] [1 0] = [-5 -4]
[c d] [-1 4]= [7 12]

so I get [a b] [-5 -4]
[-a+4c -b+4d][7 12]

Which in equation form is

a = -5 b= -4
-a + 4c = 7 -b +4d = 12

solving for c and d gives

a = -5 b = -4
c = .5 d = d = 2

Is this correct?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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Since AX=B

[a b] [1 0] = [-5 -4]
[c d] [-1 4]= [7 12]

so I get [a b] [-5 -4]
[-a+4c -b+4d][7 12]
You might want to check your matrix multiplication.

littlebu
Posts: 8
Joined: Fri Oct 22, 2010 9:23 pm
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### Re:

Yea I went through and double checked it and came up with

4b = -4
a - b = -5
4d = 12
c - d = 7

but didn't update the post.

stapel_eliz
Posts: 1628
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Yea I went through and double checked it and came up with

4b = -4
a - b = -5
4d = 12
c - d = 7
Please review how to multiply matrices. The method is demonstrated, with a little "movie", in the link provided earlier.

For instance, the top left entry of the product matrix should be the result of multipying the top row entries of A by the left column entries of X, to give you a(1) + b(-1), which you would then set equal to the top left entry of B, giving you a - b = -5.

littlebu
Posts: 8
Joined: Fri Oct 22, 2010 9:23 pm
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### Re:

Please review how to multiply matrices. The method is demonstrated, with a little "movie", in the link provided earlier.

For instance, the top left entry of the product matrix should be the result of multipying the top row entries of A by the left column entries of X, to give you a(1) + b(-1), which you would then set equal to the top left entry of B, giving you a - b = -5.
That is what I did after reviewing the link.

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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That is what I did after reviewing the link.
But you clearly did not get the same result. And the lesson isn't helping you find your error. So it really will be necessary for you to show your work, in order for us to figure out where you're going astray.

Please be complete. Thank you!

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