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Chapter 6: Q37E (page 307)

For an invertiblenxnmatrix A, what is the relationship betweenadj(A)andadj(A-1) a?

Short Answer

Expert verified

Therefore, the relationship of adj (A) and adjA-1is given by,

adjA-1=adjA-1

Step by step solution

01

 Step 1: Matrix Definition. 

Matrix is aset of numbers arranged in rows and columns so as to form a rectangulararray.

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 鈥渕 by n鈥� matrix, written 鈥�.m x n鈥�

02

To find the relationship of adj(A) and adj(A-1) 

To find the relationship,

It applies,

adjA-1=detA-1AadjA-1=1detAAadjA-1=detAA-1-1ThereforeadjA-1=adjA-1

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9. [1111112222113331114411115]
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