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The sizes of matrices A and B are given. Find the sizes of AB and BA whenever they are defined. (If the matrix product is undefined, enter UNDEFINED.)
A is of size 1 × 8, and B is of size 8 × 1.

Sagot :

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Answer:

  • AB: 1 × 1
  • BA: 8 × 8

Step-by-step explanation:

You want the dimensions of the product matrices AB and BA when the dimensions of A are 1×8, and the dimensions of B are 8×1.

Matrix multiplication

The multiplication of matrices A and B of dimensions A=[ar×ac] and B=[br×bc} will result in matrices of dimensions ...

  AB = [ar×bc} . . . . . iff ac=br

  BA = [br×ac] . . . . . iff bc=ar

That is, multiplication is only possible if the number of columns in the first matrix is equal to the number of rows in the second matrix. (In general, matrix multiplication is NOT commutative.)

Application

  A[1×8] × B[8×1] = AB[1×1] . . . . . . the product AB is a 1×1 matrix

  B[8×1] × A[1×8] = BA[8×8] . . . . . the product BA is an 8×8 matrix

The required size of the matrix AB is 1 * 1 while the size of the matrix BA is 8*8.

Given that,
The sizes of matrices A and B are given.A is of size 1 × 8, and B is of size 8 × 1. To determine the sizes of AB and BA whenever they are defined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements.

Here,

matrix A is 1 * 8  and matrix B is of 8 * 1.
So,
AB = A(1 * 8) B(8*1)= AB (1*1)
Similarly,
BA = B(8*1) A (1 * 8 ) = BA (8 * 8)

Thus, the required size of the matrix AB is 1 * 1 while the size of the matrix BA is 8*8.

Learn more about arithmetic here:

brainly.com/question/14753192E

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