1. ## Matrix

$\begin{pmatrix} -1 & -2 \\9 & 4\end{pmatrix}$ $\begin{pmatrix} 1-3k & -k \\9k & 3k+1\end{pmatrix}$

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.)

2. Hello !

Originally Posted by Air
$\begin{pmatrix} -1 & -2 \\9 & 4\end{pmatrix}$ $\begin{pmatrix} 1-3k & -k \\9k & 3k+1\end{pmatrix}$

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.)
$\begin{pmatrix} a&b \\ c&d \end{pmatrix} \begin{pmatrix} \alpha & \beta \\ \gamma & \delta \end{pmatrix}=\begin{pmatrix} a \alpha+b \gamma & a \beta+b \delta \\ c \alpha+d \gamma & c \beta+d \delta \end{pmatrix}$

3. Actually, it's like taking one row from the left matrix and multiply it with one column from the right matrix.

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

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

For note :

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