Mathematics, 22.10.2019 04:50 mandy9386
We’ve shown that matrix multiplication is generally not commutative, meaning that as a general rule for two
matrices a and b, a ⋅ b ≠ b ⋅ a. explain why f ⋅ g = g ⋅ f in each of the following examples.
a. f = 3
2 0
, g = 6
4 0
b. f =
1 3 2
3 1 2
4 3 2
, g =
0 0 0
0 0 0
0 0 0
c. f =
1 3 2
3 1 2
4 3 2
, g =
1 0 0
0 1 0
0 0 1
d. f =
1 3 2
3 1 2
4 3 2
, g =
3 0 0
0 3 0
0 0 3
Answers: 1
![G=\left[\begin{array}{ccc}2&6\\4&0\end{array}\right] =2\left[\begin{array}{ccc}1&3\\2&0\end{array}\right] =2F](/tpl/images/0340/1503/3f5d2.png)
![G=\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right] =3\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =3Id](/tpl/images/0340/1503/a848c.png)
.
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We’ve shown that matrix multiplication is generally not commutative, meaning that as a general rule...
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