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...
Select one of the women listed in Felders (1996) book (e.g., Eleanor Roosevelt, Margaret Sanger, Harriet Tubman, Rosa Parks) and read a more extensive biography about her. To what extent did she...
The Kelly Services, Inc., and Subsidiaries statements of earnings from its 2008 annual report are presented in Exhibit 5-4. Required a. Using the statements of earnings, prepare a vertical...
estion 18 yet swered rked out of Sacrificing ratio is used to distribute____ in case of admission of a partner. Flag estion a. Revaluation profit or loss b. Goodwill c. Old partners' capital or...
Consider the following 0x86 program: .data array DWORD 1,2,3,4,5,6,7,8,9 aravSize -(S-array)/4 ; array .code main PROC mov ecx,arraySize-1 mov esi.OFFSET array L1: mov eax. [esi] sda mov bx,2 idiv bx...
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.
Processing Past the Point of Separation Style Company manufactures three items, S1, S2, and S3, which are used in the production of fabrics. Each item can be sold at the point that all three are...
8. [1.5 pts] We want to design a plastic bottle. It will have inner diameter d1 and outer diameter d2 so that the thickness becomes t=(d2-d1)/2. The inner diameter is determined as 10 cm. The...
The perimeter of the rectangle below is 106 units. Find the value of y. 3y+3 2y | y-0
1 . Ameya made 4 0 % of investment in personal business, 2 0 % in stocks and the rest in mutual funds. There are 2 0 % , 1 0 % and 1 5 % of chances in obtaining profit in personal business, stocks...
4. We are given the following joint distribution over the random variables A, B, C, and D. Please answer the following questions. Show the necessary tables. You can (and should) share computations...
(f) It is hypothesized that for t> 400 s the relation between t and h is of the form where k and n are constants. h=kt (i) Outline how, using a graphical technique, you would verify this hypothesis.
It is possible to make syndiotactic polystyrene, although most polystyrene is atactic. Syndiotactic polystyrene melts at 2708C while atactic polystyrene melts closer to 2408C. (a) Why might this...
What are current assets and current liabilities? How are they different from non-current assets and non-current liabilities?
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...
How do warehouses and distribution centers differ? What is cross-docking and why might a company choose to cross-dock a product? What kinds of products can be delivered electronically? What kinds...
Strawberry Inc. has historically been an all-equity firm. The analyst expects EBIT to be $1.5B in perpetuity starting one year from now. The cost of equity for the company is 11.5% and the tax rate...
Guzman company received a 60- day, 5 % note for 54,000 dated July 12 from a customer on account. Determine the due date on note. Determine the maturity value of the note and journalize the entry of...

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