\(\displaystyle \mbox{Let }\, A\, =\, \left[\begin{array}{rr}0&-2\\7&-6\end{array}\right]\)
(i) Write A as a product of 4 elementary matrices.
(ii) Write A^-1 as a product of 4 elementary matrices.
I have 94% of the values right but I'm not entirely sure where I'm going wrong. The final row reduction of the matrix is this:
\(\displaystyle \begin{pmatrix}1&-\frac{6}{7}\\ 0&1\end{pmatrix}\)
to
\(\displaystyle \begin{pmatrix}1&0\\ 0&1\end{pmatrix}\)
This corresponds to subtracting -6/7 of the second row from the first.
I thought the elementary matrix corresponding to this was this:
\(\displaystyle \begin{pmatrix}1&-\frac{6}{7}\\ 0&1\end{pmatrix}\)
I think this is where I have made the mistake. How exactly would I express the final operation as an elementary matrix? If this is correct, could anyone be so kind to tell me where I've gone wrong.
Thank you!
(i) Write A as a product of 4 elementary matrices.
(ii) Write A^-1 as a product of 4 elementary matrices.
I have 94% of the values right but I'm not entirely sure where I'm going wrong. The final row reduction of the matrix is this:
\(\displaystyle \begin{pmatrix}1&-\frac{6}{7}\\ 0&1\end{pmatrix}\)
to
\(\displaystyle \begin{pmatrix}1&0\\ 0&1\end{pmatrix}\)
This corresponds to subtracting -6/7 of the second row from the first.
I thought the elementary matrix corresponding to this was this:
\(\displaystyle \begin{pmatrix}1&-\frac{6}{7}\\ 0&1\end{pmatrix}\)
I think this is where I have made the mistake. How exactly would I express the final operation as an elementary matrix? If this is correct, could anyone be so kind to tell me where I've gone wrong.
Thank you!
Attachments
Last edited: