Multiplying a matrix by another matrix
Multiplying a matrix by another matrix
Lessons
Notes:
In this section we will learn how to multiply two matrices like A $\cdot$ B together.
A $n$tuple is an ordered list of $n$ numbers. For example,
(1,2,3,4) is an ordered quadruple with 4 numbers, and (1,2,3) is an ordered triple with 3 numbers. We usually specify each ordered $n$tuple as a variable with an arrow on top. For example,
$\vec{x}=(1,2,3,4)$
If we have 2 ordered $n$tuples, then we can find the dot product. The dot product is summation of all the product of each corresponding entries. For example, let
$\vec{a}=(1,2,3)$ and $\vec{b}=(2,2,2)$.
If we do the dot product of $\vec{a}$ and $\vec{b}$ and ,then we will get the following:
$\vec{a}\cdot\vec{b}=(1,2,3)\cdot(2,2,2)$
$=1\cdot2+2\cdot2+3\cdot2$
$=2+4+6$
$=12$
When we want to multiply a matrix by a matrix, we want to think of each row and column as a $n$tuple. To be exact, we want to focus on the rows of the first matrix and focus on columns of the second matrix. For example,
For example, $\vec{r_1}$is the first row of the matrix with an ordered triple (1,2,3). Now to multiply these two matrices, we need to use the dot product of $\vec{r_1}$ to each column, dot product of $\vec{r_2}$ to each column, and $\vec{r_3}$ to each column. In other words

a)
Dot product

b)
Multiplying a matrix by another matrix


2.
Dot product
Find the dot product of the following ordered $n$tuples: 
3.
Multiplying matrices
Multiply the following matrices: