Find the product of the following a)(–15) × 0 × (–18) b) (–1) × (–5) × (– 4) × (– 6) say a or b
Answers
Answer:
If this is new to you, we recommend that you check out our matrix multiplication article.
What you will learn in this lesson
We will investigate the relationship between the dimensions of two matrices and the dimensions of their product. Specifically, we will see that the dimensions of the matrices must meet a certain condition for the multiplication to be defined.
When is matrix multiplication defined?
In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
To see why this is the case, consider the following two matrices:
A=\left[\begin{array}{rr}{1} &3 \\ 2& 4 \\ 2& 5 \end{array}\right]A=
⎣
⎢
⎡
1
2
2
3
4
5
⎦
⎥
⎤
and B=\left[\begin{array}{rrrr}{1} &3&2&2 \\ 2& 4&5&1 \end{array}\right]B=[
1
2
3
4
2
5
2
1
]
To find ABABA, B, we take the dot product of a row in AAA and a column in BBB. This means that the number of entries in each row of AAA must be the same as the number of entries in each column of BBB. Why?
A=\left[\begin{array}{rr}{\maroonC1} &\maroonC3 \\ 2& 4 \\ 2& 5 \end{array}\right]A=
⎣
⎢
⎡
1
2
2
3
4
5
⎦
⎥
⎤
and B=\left[\begin{array}{rrrr}{\maroonC1} &3&2&2 \\ \maroonC2& 4&5&1 \end{array}\right]B=[
1
2
3
4
2
5
2
1
]
Note that if a matrix has two
a) (-15)×0×(-18) = 0
b) (-1)×(-5)×(-4)×(-6) = 5×24 = 120
Hope it helps!!
Thank you ✌️