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Chapter 6: Q36E (page 307)

For an invertiblenxnmatrix A, what is adj(adj A)?

Short Answer

Expert verified

Therefore, the adj (adj A) is given by,

adj(adjA)=(detA)n-2A

Step by step solution

01

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 鈥渕 by n鈥� matrix, written 鈥�.m x n鈥�

02

To find

To find adj(adj A),

It applies,

adjadjA=adjdetAA-1adjadjA=detdetAA-1detAA-1-1adjadjA=detAndetA-1.1detAAadjadjA=detAn-2ATherefore,adjadjA=detAn-2A.

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Most popular questions from this chapter

Consider a 4脳4matrix A with rowsv鈫�1,v鈫�2,v鈫�3,v鈫�4. If, find the determinants in Exercises 11 through16.

12. localid="1659509477853" det[v鈫�1v鈫�2v鈫�3v鈫�4]

Use Cramer's rule to solve the systems in Exercises 22 through 24.

23. |5x1-3x2=1-6x1+7x2=0|

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

Show that the function

F[abcdefghj]=bfg

is linear in all three columns and in all three rows. See Example 6. Is F alternating on the columns? See Example 4.

IfA is an n脳n matrix of rank n-1, what is the rank of adj(A)? See Exercises 42 and 43.

See all solutions

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