Let A be an n n matrix and let be a scalar Show that det(A I) 0 if and only if Ax x for some x 0 ...

The determinant of A I will equal 0 if and only ...

Let A be an n n matrix and let be a scalar. Show that det(A

Question:

Let A be an n × n matrix and let λ be a scalar. Show that
det(A - λI) = 0
if and only if
Ax = λx for some x ≠ 0

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:49 AM

See More Questions

Let A be an n ( n real matrix, all of whose eigenvalues are real. Prove that there exist an orthogonal matrix Q and an upper triangular matrix T such that QT AQ = T. This very useful result is known...
Let A be an n n matrix and let B = A + AT and C = A - AT (a) Show that B is symmetric and C is skew-symmetric. (b) Show that every n n matrix can be represented as a sum of a symmetric matrix and a...
Let A be an n n matrix and x Rn. (a) A scalar c can also be considered as a l l matrix C = (c), and a vector be Rn can be considered as an n 1 matrix B. Although the matrix multiplication CB is...
Read the following statements. In response, state True, False or Uncertain and explain why: (a) Since resources have substitutes, nature imposes particular scarcities, not an inescapable general...
An investor in Canada purchased 100 shares of IBM on January 1 at $93.00 per share. IBM paid an annual dividend of $0.72 on December 31. The stock was sold that day as well for $100.25. The exchange...
Natsu Companys annual accounting period ends on October 31, 2019. The following information concerns the adjusting entries that need to be recorded as of that date. Entries can draw from the...
An explosion in an LNG storage tank in the process of being repaired could have occurred as the result of static electricity, malfunctioning electrical equipment, an open flame in contact with the...
The questions in this exercise give you an appreciation for the complexity of budgeting in a large multinational corporation. To answer the questions, you will need to download the Procter & Gamble...
Cuttlefish use jet propulsion to move rapidly. To do this, a cuttlefish fills its muscular mantle cavity with water and then quickly expels the water through a tube - like opening. The mass of a...
Distinguish between compatible and mapped addresses and explain their applications.
Let A and B be n n matrices and let C = AB. Use determinants to show that if either A or B is singular, then C must be singular.
Let x and y be vectors in Rn, n > 1. Show that if A = xyT then det(A) = 0.
The Thakor Corporations purchases from suppliers in a quarter are equal to 75 percent of the next quarters forecasted sales. The payables period is 60 days. Wages, taxes, and other expenses are 20...
For a business plan of a bakery: Make the operational marketing to introduce the marketing mix 4Ps: In Promotion we have to state the 4 elements -advertisement -sales promotion -public relationship...
1. [5 marks] A 72 kg person is having a tug-of-war. The rope is horizontal and 1.75 m above the ground. This person's center of mass is 1.35 m from the ground when he is in an upright standing...
One of the most notable cases of financial statement fraud involving a public company in the last five years is the case of Wirecard AG, a German payment processor and financial services provider....
Solve the equation by factoring: r2_ 5x 6=0
According to the records of a soft drink company, the bottles for their one-liter-sized products contain an average (mean) of 1.01 liters of beverage, with a standard deviation of 0.16 liters. As...
In Problem refer to the following probability tree: Suppose that c = d = e = f . Discuss the dependence or independence of events M and N. M U c+d = 1 a d N Start a + b = 1 a, b, c, d, e, f+0 M e +f...
On January 1, 2018, Khalid Ltd., which follows IAS 17, entered into an eight-year lease agreement for three dryers. Annual lease payments for the equipment are $28,500 at the beginning of each lease...
Let be an eigenvalue of a linear operator T: V V. Prove that the eigenvectors of T corresponding to are the nonzero vectors in the kernel of I - T.
Let C and D be m n matrices, and let B = (v1, v2, ..., vn) be a basis for a vector V. Show that if C[x]B = D[x]B for all x in V, then C = D.
Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) A matrix cannot be similar to itself. (b) If A is similar...
Show how binary exponentiation can be used to calculate a 128 efficiently. How many multiplications are required?
How can one tell many months the positive skew had in it?
Drug 4 mg I every 3 hours prn pain. Supplied as 10mg/10 ml. Calculate mL per dose?

Let A be an n n matrix and let be a scalar. Show that det(A

Question:

Step by Step Answer:

The determinant of A I will equal 0 if and only ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions