# Math Help - Matrix Inverses, help plz

1. ## Matrix Inverses, help plz

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

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

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

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

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

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 ....

3. 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

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

4. 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

$B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix}$ is one example
So what's $I_2$ meant to represent?

5. Originally Posted by mr fantastic
So what's $I_2$ meant to represent?
$I_2 = \left(\begin{array}{cc}1&0\\0&1\end{array}\right)$

More generally, $I_n$ is the nxn square matrices with 1 in its leading diagonal (i.e. from top-left to bottom-right).

6. 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

$B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix}$ is one example
Yes, I did misunderstand the question.

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

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

One way to do it would be to assume that $B = \begin{bmatrix} a& b & c & d \\ e &f & g &h \end{bmatrix}$, 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!)

8. Originally Posted by SimonM
That is indeed how I did it (same letters and everything!)
Well you know what they say about great minds ......

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

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

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

A little clarifications would be nice, totally dont understand this question at all.
By inspection one such matrix is:

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

CB

11. ahhh I see thank you guys.