Find the $2 \times 2$ matrix $\bold{A}$ such that

Question

\[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}\]
and
\[\bold{A} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -7 \\ 4 \end{pmatrix}.\]

Regular:

Find the 2 x 2 matrix A such that:

A<6,-1> = <13,-26>
&
A<1,4> =<23,4>.

I am struggling to solve this problem, any help would be appreciated!

Answer 1

The numbers in your LaTeX don't seem to agree with the "regular" section, so I'll ignore them. You want A with rows (a b) and (c d) such that

6a-b = 13
6c-d = -26
a+4b = 23
c+4d = 4

I get rows (3 5) and (-4 2)

Check:

http://www.wolframalpha.com/input/?i=%7B%7B3,5%7D,%7B-4,2%7D%7D*%7B%7B6,1%7D,%7B-1,4%7D%7D

Answer 2

My bad! Thanks for the help! I was able to figure out the latex problem accordingly :)