1. ## Solving matrix equations

P is a 2 times 2 matrix.Determine p if

2. Have you even tried to do this yourself? It's very straight forward.

$\displaystyle 3\begin{bmatrix}1 & 0 \\ 2 & 4\end{bmatrix}- 2P= \begin{bmatrix}-2 & -3 \\ 4 & -5\end{bmatrix]$.

Since P must be a 2x2 matrix in order to be able to subtract 2P, write it as [tex]\begin{bmatrix}a & b \\ c & d\end{bmatrix}:

$\displaystyle 3\begin{bmatrix}1 & 0 \\ 2 & 4\end{bmatrix}- 2\begin{bmatrix}a & b \\ c & d\end= \begin{bmatrix}-2 & -3 \\ 4 & -5\end{bmatrix]$.

Do the indicated calculations and you will have 4 separate linear equations for a, b, c, and d. For example, one equation is 1- 2a= -2. That's easy to solve.

3. Originally Posted by mastermin346
P is a 2 times 2 matrix.Determine p if
let $\displaystyle \begin{bmatrix} 1 & 0\\ 2 & 4 \end{bmatrix}$ be A

and let
$\displaystyle \begin{bmatrix} -2 & -3\\ 4 & -5 \end{bmatrix}$ be C.

So we have $\displaystyle 3A-2P=C$

to find P, rearange it

$\displaystyle -P=\frac{C-3A}{2}$

$\displaystyle P=-\frac{C-3A}{2}$

Can you do it now?