# Matrix

• Jun 19th 2008, 12:36 AM
Simplicity
Matrix
$\displaystyle \begin{pmatrix} -1 & -2 \\9 & 4\end{pmatrix}$$\displaystyle \begin{pmatrix} 1-3k & -k \\9k & 3k+1\end{pmatrix} What does that equal? Thanks in advance. (EDIT: Sorry, I didn't realise that I was on Calculus forum hence posted incorrect thread. Thought I was in Urgent Homework Help forum.) • Jun 19th 2008, 12:47 AM Moo Hello ! Quote: Originally Posted by Air \displaystyle \begin{pmatrix} -1 & -2 \\9 & 4\end{pmatrix}$$\displaystyle \begin{pmatrix} 1-3k & -k \\9k & 3k+1\end{pmatrix}$

What does that equal? Thanks in advance.

(EDIT: Sorry, I didn't realise that I was on Calculus forum hence posted incorrect thread. Thought I was in Urgent Homework Help forum.)

$\displaystyle \begin{pmatrix} a&b \\ c&d \end{pmatrix} \begin{pmatrix} \alpha & \beta \\ \gamma & \delta \end{pmatrix}=\begin{pmatrix} a \alpha+b \gamma & a \beta+b \delta \\ c \alpha+d \gamma & c \beta+d \delta \end{pmatrix}$
• Jun 19th 2008, 12:51 AM
Moo
Actually, it's like taking one row from the left matrix and multiply it with one column from the right matrix.

$\displaystyle (a \quad b)\begin{pmatrix} \alpha \\ \gamma \end{pmatrix}$ will give you the $\displaystyle a_{11}$ element of the resulting matrix.

$\displaystyle (a \quad b) \begin{pmatrix} \beta \\ \delta \end{pmatrix}$ will give you the $\displaystyle a_{12}$ element of the resulting matrix.

For note :

$\displaystyle \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}$