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Chapter 6: Q35E (page 307)

For an invertible nxn matrix A, what is the relationship between det (A) and det (A)?

Short Answer

Expert verified

Therefore, the relationship of det (A) and det (A) is given by,

detadjA=detAn-1

Step by step solution

01

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  and

To find the relationship,

We know that,

adjA=detAA-1.

Therefore,

detadjA=det(detAA-1)detadjA=detAndetA-1detadjA=detAn-1

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Most popular questions from this chapter

If all the diagonal entries of an n脳nmatrix Aare odd integers and all the other entries are even integers, thenA must be an invertible matrix.

The matrix [k214k-1-2111] is invertible for all positive constantsk.

Find all 2脳2 matrices Asuch thatadj(A)=AT.

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

positive or negative? How can you tell? Do not use technology.

a. Find a noninvertible 2脳2matrix whose entries are four distinct prime numbers, or explain why no such matrix exists.

b. Find a noninvertible 3脳3matrix whose entries are nine distinct prime numbers, or explain why no such matrix exists.
See all solutions

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