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Q38E

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Linear Algebra With Applications
Found in: Page 307
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

For two invertible nxn matrices A and B , what is the relationship between adj(A),adj(B), and adj(AB)?

Therefore, the relationship of adjA,adjB and adjAB is given by,

adj AB=adj B adj A.

See the step by step solution

Step by Step Solution

Step 1: Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “.mxn”

Step 2: To find the relationship of  and

To find the relationship,

It applies,

adjAB=det( AB(AB)-1 adjAB=det A det BB-1A-1adjAB=det BB-1det AA-1ThereforeadjAB=adj BadjA.

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