Explanation Calculation: For two matrices say A and B said to be commutative if and only if they must follow A B = B A . Let assume the matrices A and B as, A = [ 1 2 3 4 ] and B = [ 5 6 7 8 ] Multiply matrix A with B A B = [ 1 2 3 4 ] [ 5 6 7 8 ] = [ 1 ⋅ 5 + 2 ⋅ 7 1 ⋅ 6 + 2 ⋅ 8 3 ⋅ 5 + 4 ⋅ 7 3 ⋅ 6 + 4 ⋅ 8 ] = [ 19 22 43 50 ] Now, Multiply matrix B with A . B A = [ 5 6 7 8 ] [ 1 2 3 4 ] = [ 5 ⋅ 1 + 6 ⋅ 3 5 ⋅ 2 + 6 ⋅ 4 7 ⋅ 1 + 8 ⋅ 3 7 ⋅ 2 + 8 ⋅ 4 ] = [ 23 34 31 48 ] Since, matrix A B and B A are not equal matrix multiplication is not commutative. For matrix to be associative it must follow. ( A B ) C = A ( B C ) Let assume matrix C as C = [ 4 5 6 7 ] Now matrix ( A B ) C is,

MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

8th Edition

ISBN: 9780357537343

Author: Johnson

Publisher: CENGAGE L

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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The commutative and associative nature of matrix.

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MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

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The commutative and associative nature of matrix.

Solution Summary: The author explains that matrix multiplication is not commutative but it is associative.

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To find: The commutative and associative nature of matrix.

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To find:

The commutative and associative nature of matrix.