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Chapter 6: Q24E (page 309)

If is any noninvertible square matrix, then detA=det(rrefA).

Short Answer

Expert verified

Therefore,

detA=det(rrefA)

Yes, the given statement is true.

Step by step solution

01

Orthogonal Matrix Definition. 

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

02

To check whether the given condition is true or false.

Given condition,

detA=det(rrefA).

If is a non-invertible matrix,

Then

det A = 0.

detA=detrrefA

Therefore, the given condition satisfied. So, the given statement is true.

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Most popular questions from this chapter

In Exercises 62 through 64, consider a function D from 鈩�2脳2 to鈩� that is linear in both columns and alternating on the columns. See Examples 4 and 6 and the subsequent discussions. Assume thatD(l2)=1.


62. Show thatD(A)=0for any2脳2matrix whose two columns are equal.

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

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

Consider a4脳4matrix A with rowsv鈫�1,v鈫�2,v鈫�3,v鈫�4. If det(A) = 8, find the determinants in Exercises 11 through16.

13. det[v鈫�1v鈫�2v鈫�3v鈫�4]

Show that A(adjA)=0=(adjA)Afor all noninvertible n脳nmatrices A. See Exercise 42.

IfA is a 4脳4 matrix whose entries are all 1 or -1 , then detAmust be divisible by 8 (i.e., detA=8kfor some integer k).
See all solutions

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