If A is a square matrix, show that det A = 0 if and only if some

Question:

If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.

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: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Question Posted: Jun 21, 2016 06:43 AM

See More Questions

Let A be a square matrix that can be partitioned as where P and S are square matrices. Such a matrix is said to be in block (upper) triangular form. Prove that det A = (det P)(det S) o S
Mark each of the following statements true or false: (a) For all square matrices A, det(-A) = -det A. (b) If A and B are n n matrices, then det(AB) = det (BA). (c) If A and B are n n matrices whose...
Let A be a nonsingular square matrix. (a) Prove that the product of the singular values of A equals the absolute value of its determinant: 1 2 ... n = |det A|. (b) Does their sum equal the absolute...
Boeing Company was scheduled to deliver several of its 747-400 jumbo jetliners to Northwest Airlines by December 31, 1988. Northwest set that deadline because it needed the $16 million in investment...
Distinguish between a report qualified as to opinion only and one with both a scope and opinion qualification.
Explain the main components of a grievance procedure. LO9
Visualize yourself as a Whole Foods store manager. What might be the unintended negative consequences of allowing employees to split the money saved from minimizing the number of workers on a team?...
a. Prepare line graphs of each of the six expenditure categories. Indicate whether each category appears to be stationary or nonstationary. b. Use Holts method to create models for each expenditure...
Requieu UMTALUN Exercise 6-21B Complete the accounting cycle using inventory transactions (L06-2, 6-3, 6-5, 6-6, 6-7) (The following information applies to the questions displayed below.) On January...
Mariam is a trader. On 1 March 202 the balances in her cash book were: Cash $100 debit Bank $494 credit The following transactions took place in March 202: March 4 Paid for repairs to office...
In each case, find a basis for V that includes the vector v. (a) V = R3, v = (0, 1, 1) (b) V = P2, v = x2 - x + 1
Let D, I, and X denote finite, nonempty sets of vectors in a vector space V. Assume that D is dependent and / is independent. In each case answer yes or no, and defend your answer. (a) If X D, must...
I. Discuss installing Internet connections, which requires using leased lines or other data channels provided by common carriers, and therefore these connections are usually permanent and secured...
solve for x 4 . 0 a 2 = 2 . 0 a x
BUSINESS SOLUTIONS Comparative Balance Sheets March 3 1 , 2 0 2 2 December 3 1 , 2 0 2 1 Assets Cash $ 8 4 , 7 8 7 $ 5 7 , 8 7 2 Accounts receivable 2 4 , 2 6 7 5 , 0 6 8 Inventory 6 1 4 0 Computer...
Solve:z-18=-103.
Complete the social penetration exercise and post your reactions in the discussion. PIRATION Purpose: 1. To help you understand the breadth and depth of self-disclosure. 2. To help you see the...
The implicit equation of x = sin ( t ) and y = 2 cos ( t ) is:
Calculate the pH at the points in the titration of 20.00 mL of 0.275 M KOH when (a) 15.00 mL and (b) 20.00 mL of 0.350 M HCl have been added.
A consultant is beginning work on three projects. The expected profits from these projects are $50,000, $72,000, and $40,000. The associated standard deviations are $10,000, $12,000, and $9,000....
A certain forest is divided into three height classes and has a growth matrix between harvests given by If the price of trees in the second class is $30 and the price of trees in the third class is...
In Example 1, what must the ratio of the prices p2: p3: p4: p5: p6 be in order that the yields Yldk, k = 2, 3, 4, 5, 6, all be the same? (In this case, any sustainable harvesting policy will produce...
For the optimal sustainable harvesting policy described in Theorem 11.10.2, how many trees are removed from the forest during each harvest?
Oct. 31: Paid salaries, $45,000 ( 75% selling, 25% administrtive). Data table Data table them to retail stores. The company has three inventory items: and floor lamps. RLC uses a perpetual inventory...
question 1- You borrow a simple loan of SR 500,000, interest rate is 20%, it matures in one year. what's the yied to maturity? question 2- calculate_i for One-Year Discount Bond with price(p) =...
Taste of Muscat is a reputed chain of restaurants operating in Oman. Assume You are working as a management accountant for this restaurant chain which is specialized in all types of Arabic food. Your...

If A is a square matrix, show that det A = 0 if and only if some

Question:

Step by Step Answer:

We have det A 0 if and only if A is not invert...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions