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Mathematics

2 answers:

LenaWriter [7]2 years ago

8 0

Answer:

First one is: Expanded form; 2*2*2. Standard form; 8

Second one is: Expanded form; (3*3)*(e*e*e). Standard form; 9*3e

Step-by-step explanation:

Tpy6a [65]2 years ago

6 0

2^3:
a) 2 x 2 x 2
b) 8

3^2 x e^3:
a) 3 x 3 x e x e x e
b) 9e^3

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Is matrix multiplication comutative?

konstantin123 [22]

Answer:

Matrix multiplication is not conmutative

Step-by-step explanation:

The matrix multiplication can be performed if the number of columns of the first matrix is equal to the number of rows of the second matrix

Let A with dimension mxn and B with dimension nxp represent two matrix

The multiplication of A by B is a matrix C with dimension mxp, but the multiplication of B by A is can't be calculated because the number of columns of B is not the number of rows of A. Therefore, you can notice that is not conmutative in general.

But even if the multiplication of AB and BA is defined (For example if A and B are squared matrix of 2x2) the multiplication is not necessary conmutative.

The matrix multiplication result is a matrix which entries are given by dot product of the corresponding row of the first matrix and the corresponding column of the second matrix:

$A=\left[\begin{array}{ccc}a11&a12\\a21&a22\end{array}\right]\\B= \left[\begin{array}{ccc}b11&b12\\b21&b22\end{array}\right]\\AB = \left[\begin{array}{ccc}a11b11+a12b21&a11b12+a12b22\\a21b11+a22b21&a21b12+a22b22\end{array}\right]\\\\BA=\left[\begin{array}{ccc}b11a11+b12a21&b11a12+b12a22\\b21a11+b22ba21&b21a12+b22a22\end{array}\right]$