Question: Prove that A is a singular matrix if and only if 0 is an eigenvalue.

Prove that A is a singular matrix if and only if 0 is an eigenvalue.

Step by Step Solution

★★★★★

3.58 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To conclude I can say that recall ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

952-M-L-A-E (2609).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let A be an n n matrix. Prove that A is singular if and only if = 0 is an eigen value of A.

Q:

If A is an n n matrix, prove that A is nonsingular if and only if the linear system Ax = b has a unique solution for every n 1 matrix b.

Q:

Prove that A = AT is a symmetric n x n matrix if and only if {A v) w = v (A w) for all v. w Rn.

Q:

1. Let A = 90 3 552 Find the characteristic polynomial of A and guess one of its roots by looking at integer divisors of the constant term. Find an eigenvector corresponding to this eigenvalue, and...

Q:

1. Find the eigenvalues and corresponding eigenspaces for each of the following matrices: 2. Let A be an n x n matrix (a) Prove that A is singular if and only if A = 0 is an eigenvalue of A. (b) Lal...

Q:

In this problem, you'll work with some new definitions, one of which you've actually seen before. Before attempting the problem, read the definitions carefully and recall some of the work you've done...

Q:

In this problem, you'll work with some new definitions, one of which you've actually seen before. Before attempting the problem, read the definitions carefully and recall some of the work you've done...

Q:

If A is a 4 4 matrix of rank 1 and = 0 is an eigenvalue of multiplicity 3, then A is defective. In the case of a true statement, explain or prove your answer. In the case of a false statement, give...

Q:

If A is a 4 4 matrix of rank 3 and = 0 is an eigenvalue of multiplicity 3, then A is diagonalizable. In the case of a true statement, explain or prove your answer. In the case of a false statement,...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Modify the Category form by changing the sales markup text box control to a combo box control that lists choices of 100%, 125%, 150%, 175%, and 200%. Format the text box control to a percent format...

Q:

Prisoners dilemma is very significant in Oligopoly market where there are around 45 large firms and each spend huge amount of money on advertsisment and increase sales Product type is similar and...

Q:

A company usually would not want to issue convertible securities if its stock is undervalued in the market

Q:

Why are independent courts important for a wellfunctioning economy?

Q:

The kings coinmaster boxes his coins 500 to a box and puts 1 counterfeit coin in each box. The king is suspicious, but, instead of testing all the coins in 1 box, he tests 1 coin chosen at random out...

Q:

In one of the first studies of the Poisson distribution, von Bortkiewicz7 considered the frequency of deaths from kicks in the Prussian army corps. From the study of 14 corps over a 20-year period,...

Q:

A manufactured lot of brass turnbuckles has S items of which D are defective. A sample of s items is drawn without replacement. Let X be a random variable that gives the number of defective items in...

Q:

Jerry just purchased a bond paying semiannual interest for a price of $1, 000. Yields on bonds of similar risk are 10.8% The bond has a face value of $1, 000. Based on this information, the coupon...

Q:

Watkins Resources faces a smooth annual demand for cash of $1.70 million, incurs transaction costs of $65 every time the firm sells marketable securities, and can earn 2.7 percent on its marketable...

Q:

Include the correct Excel Forumulas to solve this question