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

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

To find the matrix $\bold{A}$, we can use the fact that multiplying a matrix by a column vector gives us a linear combination of the columns of the matrix. In other words, we can write the equation as:

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

Since the first column of $\bold{A}$ is multiplied by 1 and the second column is multiplied by 0, we can conclude that the first column of $\bold{A}$ is $\begin{pmatrix} 1 \\ 2 \end{pmatrix}$.

Similarly, we have:

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

This tells us that the second column of $\bold{A}$ is $\begin{pmatrix} -7 \\ 4 \end{pmatrix}$.

Therefore, the matrix $\bold{A}$ is given by:

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

Why not type in the regular way like you did here ?

http://www.jiskha.com/display.cgi?id=1486616450

I can't read your post the way it was typed.