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 littlebu December 6th, 2010 02:52 PM

Help with Matrix problem

I do not now how to do these types of problems. Could somebody point me in the right direction?

Find the matrix A such that

A[ 1 0 ] = [ -5 -4]
[ -1 4] = [ 7 12]

hint: let A = [a b]
[c d]

 The Chaz December 6th, 2010 03:20 PM

Re: Help with Matrix problem

Do you know how to do matrix multiplication?
$$\begin{array}{cc} a & b \\ c & d \end{array}$*$\begin{array}{cc} 1 & 0 \\ -1 & 4 \end{array}$ = $\begin{array}{cc} a-b & 4b \\ c-d & 4d \end{array}$$

Set this equal to the given matrix,
$$\begin{array}{cc} -5 & -4 \\ 7 & 12 \end{array}$$

then solve by setting corresponding elements equal to each other.

 littlebu December 6th, 2010 03:33 PM

Re: Help with Matrix problem

Quote:
 Originally Posted by The Chaz Do you know how to do matrix multiplication? $$\begin{array}{cc} a & b \\ c & d \end{array}$*$\begin{array}{cc} 1 & 0 \\ -1 & 4 \end{array}$ = $\begin{array}{cc} a-b & 4b \\ c-d & 4d \end{array}$$ Set this equal to the given matrix, $$\begin{array}{cc} -5 & -4 \\ 7 & 12 \end{array}$$ then solve by setting corresponding elements equal to each other.

I get to here:

$$\begin{array}{cc} -5 & -4 \\ 7 & 12 \end{array}$$

Then:

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?

I am new to this, just trying to figure it out by following along in a book.

 greg1313 December 6th, 2010 03:51 PM

Re: Help with Matrix problem

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

 The Chaz December 6th, 2010 04:10 PM

Re: Help with Matrix problem

Quote:
 Originally Posted by littlebu ...I am new to this, just trying to figure it out by following along in a book.
Compare the matrices in my reply with the statements in greg1313's post

 soroban December 6th, 2010 04:11 PM

Re: Help with Matrix problem

Hello, littlebu!

It would help if you didn't scatter your work . . .

Quote:
 $\text{Find the matrix }A\text{ such that: }\;A\,\cdot\, \begin{bmatrix} 1=&0 \\ \\ \\ -1=&4\end{bmatrix} \:=\: \begin{bmatrix}-5 &-4 \\ \\ \\ 7=&12\end{bmatrix}=$ $\text{Hint: \; let }A \:=\: \begin{bmatrix}a &b \\ \\ c=&d \end{bmatrix}=$

$\text{We have: }\;\begin{bmatrix} a=&b \\ \\ c=&d \end{bmatrix} \,\cdot\,\begin{bmatrix}1=&0 \\ \\ -1=&4 \end{bmatrix} \;=\;\begin{bmatrix}-5 &-4 \\ \\ 7=&12 \end{bmatrix}=$

[color=beige]. . . . . . . . . . . [/color]$\begin{bmatrix} a-b=&4b \\ \\ c-d=&4d \end{bmatrix} \:=\:\begin{bmatrix}-5 &-4 \\ \\ 7=&12 \end{bmatrix}=$

$\text{And we have four equations: }\;\begin{array}{cccccccccc}(1)=&a-b=&-5=&(3)=&4b=&-4 \\ \\ \\ (2)=&c-d=&7=&(4)=&4d=&12 \end{array}=$

$\text{Solve the system and we get: }\;\begin{Bmatrix}\;a=&-6 \; \\ \\ \\ \;b=&-1\; \\ \\ \\ \;c=&10\; \\ \\ \\ \;d=&3\; \end{Bmatrix} \;\;\;\Rightarrow\;\;\;A \:=\:\begin{bmatrix} -6 &-1 \\ \\ \\ 10=&3\end{bmatrix}=$

 littlebu December 6th, 2010 05:13 PM

Re: Help with Matrix problem

Thanks for the replies everyone, this is really helpful and makes sense now. This forum is fantastic, it is hard to "teach" yourself from a book when you don't know what to do, thanks again for the help I have a feeling I am going to be asking a lot of questions here. Hope you all don't get annoyed with me lol.

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