Consider the number of columns of the first matrix and the number of rows of the second matrix. Are they equal? What does that mean?
-1 & 0 1 & 5 0 & -3
Practice makes perfect
We need to recall that the multiplication of two matrices is defined only if the number of columns in the first matrix is equal to the number of rows in the second matrix. Moreover, when multiplying matrices A and B, the resulting matrix will have as many rows as A and as many columns as B.
Let's consider the given matrices. Since 2 = 2, the number of columns of the first matrix is equal to the number of rows of the second one. Therefore, the multiplication is defined and the dimensions of the product will be 3 * 2.
[
ccc
1 & 0 -1 & -5 0 & 3
]
and
[
cc
-1 &0
0 &-1
]
cc
3* 2 & 2* 2
Multiplication of matrices is done using a process called the dot product. It follows a pattern of multiplying and adding terms across the rows of the first matrix and down the columns of the second one.
[
ccc
a& b c&d e&f
]
*
[
cc
g&h i&j
]
=
[
cc
a g+ b i&ah+bj cg+di&ch+dj eg+fi&eh+fj
]
Let's calculate it!
