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.
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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 ....Quote:
Originally Posted by p00ndawg
I think you misunderstood the question. There is a matrix which satisfiesQuote:
Originally Posted by mr fantastic
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?Quote:
Originally Posted by SimonM
$\displaystyle I_2 = \left(\begin{array}{cc}1&0\\0&1\end{array}\right)$Quote:
Originally Posted by mr fantastic
More generally, $\displaystyle I_n$ is the nxn square matrices with 1 in its leading diagonal (i.e. from top-left to bottom-right).
Yes, I did misunderstand the question.Quote:
Originally Posted by SimonM
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!)Quote:
Originally Posted by mr fantastic
Well you know what they say about great minds ......Quote:
Originally Posted by SimonM
... and foolsQuote:
Originally Posted by mr fantastic
By inspection one such matrix is:Quote:
Originally Posted by p00ndawg
$\displaystyle
\begin{bmatrix}-1&0 &0&0\\ 0&1&0&0 \end{bmatrix}
$
CB
ahhh I see thank you guys.
