Answer:
[tex]\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right] \left[\begin{array}{ccc}c\\d\end{array}\right] =\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right][/tex]
This tells us that:
[tex]A=\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right][/tex]
[tex]b=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right][/tex]
Step-by-step explanation:
So we are saying we have scalars, c and d, such that:
[tex]c\left[\begin{array}{ccc}5\\5\\ 3\end{array}\right]+d\left[\begin{array}{ccc}7\\-8\\-9\end{array}\right]=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right][/tex].
So we want to find a way to express this as:
Ax=b where x is the scalar vector, [tex]\left[\begin{array}{ccc}c\\d\end{array}\right][/tex].
So we can write this as:
[tex]\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right] \left[\begin{array}{ccc}c\\d\end{array}\right] =\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right][/tex]
