Matrix Inverses, help plz

• Oct 19th 2008, 06:39 PM
p00ndawg
Matrix Inverses, help plz
Let A be a 4 X 2 matrix, A = $\displaystyle \begin{bmatrix}-1&0 \\ 0 & 1 \\ 1&2\\ 2&1 \end{bmatrix}$

Is there a 2X4 matrix such that $\displaystyle BA = I_2$?

A little clarifications would be nice, totally dont understand this question at all.
• Oct 19th 2008, 07:00 PM
mr fantastic
Quote:

Originally Posted by p00ndawg
Let A be a 4 X 2 matrix, A = $\displaystyle \begin{bmatrix}-1&0 \\ 0 & 1 \\ 1&2\\ 2&1 \end{bmatrix}$

Is there a 2X4 matrix such that $\displaystyle BA = I_2$?

A little clarifications would be nice, totally dont understand this question at all.

A necessary (but not sufficient) condition for the inverse of a matrix to exist is that the matrix must be square ....
• Oct 19th 2008, 11:55 PM
SimonM
Quote:

Originally Posted by mr fantastic
A necessary (but not sufficient) condition for the inverse of a matrix to exist is that the matrix must be square ....

I think you misunderstood the question. There is a matrix which satisfies

The question is asking can we find a matrix which satisfies the equation and we can

$\displaystyle B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix}$ is one example
• Oct 20th 2008, 12:23 AM
mr fantastic
Quote:

Originally Posted by SimonM
I think you misunderstood the question. There is a matrix which satisfies

The question is asking can we find a matrix which satisfies the equation and we can

$\displaystyle B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix}$ is one example

So what's $\displaystyle I_2$ meant to represent?
• Oct 20th 2008, 12:29 AM
bumcheekcity
Quote:

Originally Posted by mr fantastic
So what's $\displaystyle I_2$ meant to represent?

$\displaystyle I_2 = \left(\begin{array}{cc}1&0\\0&1\end{array}\right)$

More generally, $\displaystyle I_n$ is the nxn square matrices with 1 in its leading diagonal (i.e. from top-left to bottom-right).
• Oct 20th 2008, 12:39 AM
mr fantastic
Quote:

Originally Posted by SimonM
I think you misunderstood the question. There is a matrix which satisfies

The question is asking can we find a matrix which satisfies the equation and we can

$\displaystyle B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix}$ is one example

Yes, I did misunderstand the question.

One way to do it would be to assume that $\displaystyle B = \begin{bmatrix} a& b & c & d \\ e &f & g &h \end{bmatrix}$, do the multiplication, equate entries and solve the resulting four linear equations (infinite number of solutions).
• Oct 20th 2008, 12:40 AM
SimonM
Quote:

Originally Posted by mr fantastic
Yes, I did misunderstand the question.

One way to do it would be to assume that $\displaystyle B = \begin{bmatrix} a& b & c & d \\ e &f & g &h \end{bmatrix}$, do the multiplication, equate entries and solve the resulting four linear equations (infinite number of solutions).

That is indeed how I did it (same letters and everything!)
• Oct 20th 2008, 12:45 AM
mr fantastic
Quote:

Originally Posted by SimonM
That is indeed how I did it (same letters and everything!)

Well you know what they say about great minds ......
• Oct 20th 2008, 12:46 AM
SimonM
Quote:

Originally Posted by mr fantastic
Well you know what they say about great minds ......

... and fools
• Oct 20th 2008, 02:51 AM
CaptainBlack
Quote:

Originally Posted by p00ndawg
Let A be a 4 X 2 matrix, A = $\displaystyle \begin{bmatrix}-1&0 \\ 0 & 1 \\ 1&2\\ 2&1 \end{bmatrix}$

Is there a 2X4 matrix such that $\displaystyle BA = I_2$?

A little clarifications would be nice, totally dont understand this question at all.

By inspection one such matrix is:

$\displaystyle \begin{bmatrix}-1&0 &0&0\\ 0&1&0&0 \end{bmatrix}$

CB
• Oct 20th 2008, 04:52 AM
p00ndawg
ahhh I see thank you guys.