Question: Let A be a 3 ( 3 matrix with first row [k 0 0] for some nonzero real number k. Prove that k is an

Let A be a 3 ( 3 matrix with first row [k 0 0] for some nonzero real number k. Prove that k is an eigenvalue of A?

Step by Step Solution

★★★★★

3.38 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let Then kI 3 A has its fir... 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

951-M-L-A-L-S (7117).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let A be a 3 ( 4 matrix, let v1 and v2 be vectors in, and let w = v1 + v2. Suppose v1 = Au1 and v2 = Au2 for some vectors u1 and u2 in. What fact allows you to conclude that the system Ax = w is...

Q:

Let A be a m à n matrix which represents (exercise 3.253) the payoff function of a two-person zero-sum game in which player 1 has m pure strategies and player 2 has n strategies. Let Z be the...

Q:

Let A be a 5 ( 3 matrix, let y be a vector in, and let z be a vector in. Suppose Ay = z. What fact allows you to conclude that the system Ax = 5z is consistent? 23

Q:

Question 6. Compute the LU factorization of each of the following matrices. 3 24 (a) (b) -2 2 -2 01-01-19 (c) 4 Question 7. Find the LDU decomposition of the matrix 1 1 356 -2 27 Question 8. Let A be...

Q:

Hello tutor, help needed with questions in the pictures attached below, thanks! no need for full solution, just answers to fill up the empty boxes. Quiz: Quiz #2 2.1 - 2.3 0 Score: 0 of 1 point...

Q:

Hello tutor, help needed with questions in the pictures attached below, thanks! no need for full solution, just answers to fill up the empty boxes. Quiz: Quiz #2 2.1 - 2.3 0 Score: 0 of 1 point...

Q:

5. In a matrix, the number of leading zeros in Row 2' is the number of zeros in that row to the left of the rst non-zero entry of that row (if the row contains any nonzero entry). A matrix A is...

Q:

Let P, Q be square matrices of order n and let 11,1, 11,2, . . ., u," be columns vectors in R\". Which of the following statements are always true? (There may have multiple answers.) C] If P, Q are...

Q:

Let P, Q be square matrices of order n and let 11,1, 11,2, . . ., u," be columns vectors in R\". Which of the following statements are always true? (There may have multiple answers.) C] If P, Q are...

Q:

1. [0/1 Points] DETAILS PREVIOUS ANSWERS 2/100 Submissions Used Identify the elementary row operation(s) being performed to obtain the new row-equivalent matrix. (Select all that apply.) Original...

Q:

On February 1, 2014, Quass Ltd. began selling electric scooters that it purchased exclusively from lonone Motors Inc. Ionone Motors offers vendor rebates based on the volume of annual sales to its...

Q:

Iqra University is considering investing in an online book ordering and information service, which will be managed by 2 employees. The following estimates relate to the costs of starting the service...

Q:

EXERCISE 7-5. Incremental Analysis Each year, Knight Motors surveys 6,000 former and prospective customers regarding satisfaction and brand awareness. For the current year, the company is considering...

Q:

Project team members are most likely to work full time on a project in which of the following organizational structures? A. Functional B. Weak matrix C. Organizational D. Project-oriented

Q:

Projectile Motion. A stone thrown downward with an initial velocity of 34.3 m/sec will travel a distance of s meters, where s(t) = 4.9t2 + 34.3t and t is in seconds. If a stone is thrown downward at...

Q:

Games in a Sports League. If there are x teams in a sports league and all the teams play each other twice, a total of N(x) games are played, where N(x) = x2 - x. A softball league has 9 teams, each...

Q:

Median Home Prices. The median price for an existing home in the United States peaked at $221,900 in 2006 (National Association of REALTORS®). The quartic function h(x) = 56.8328x4 - 1554.7494x3...

Q:

If an independent project with conventional, or normal, cash flows is being analyzed, the net present value (NPV) and internal rate of return (IRR) method agree. Projects W and X are mutually...

Q:

Consider the "robot trap" in the following figure. 1. Explain why it is so tricky for a robot to get to location g . You must explain what the current robot does as well as why it is difficult to...

Q:

An asset costs $860,000 and will be depreciated in a straight-line manner over its four-year life. It will have no salvage value. The corporate tax rate is 23 percent and the appropriate interest...