Let A be an m ( n matrix. Prove that if AT A is nonsingular, then rank

Question:

Let A be an m ( n matrix. Prove that if AT A is nonsingular, then rank A = n.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:03 AM

See More Questions

Let A be an m x n matrix with rank A = n. (a) Prove that the matrix P = A(ATA)~l AT is a projection matrix, meaning that P2 = P, cf. Exercise 2.5.8. (b) Construct the projection matrix corresponding...
Let A be an m x n matrix. Show that (a) If x N(ATA), then Ax is in both R(A) and N(AT). (b) N(ATA) = N(A). (c) A and ATA have the same rank. (d) If A has linearly independent columns, then ATA is...
Let P = A(ATA)-1 AT, where A is an m n matrix of rank /;. (a) Show that P2 = P. (b) Prove Pk = P for k = 1,2 (c) Show that P is symmetric. [If B is nonsingular, then (B-1)T = (BT)-1]
What other types of contingency planning should Matt and Chris include to make the report comprehensive? Please explain the relevance of each suggestion.
A blood bank wants to determine the least expensive way to transport available blood donations from Pittsburg and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. Figure...
LO2 As stated in the text, the federal income tax is the largest revenue-producing tax in use in the United States. Why do you think the income tax produces more revenue than any other tax?
E3-4 Correction of consolidated net income Liong Corporation paid $2,500,000 in cash for an 80 percent interest in Taro Corporation on January 1, 2016, when the book value of Taros net assets was...
You have been assigned to the audit of Oshkosh Truck Corporation. The company is the leading manufacturer of fire trucks and heavy duty army trucks. All of the basic components are warranted for...
Future value is best described as: The sum of dollars-in discounted to time zero. None of the answers are correct. The sum of dollars-out discounted to time zero. The value of a dollar-in or a...
TeleTech Corporation manufactures two different fax machines for the business market. Cost estimates for the two models for the current year are as follows: The firms management expects to operate at...
Suppose that A is an n ( n matrix and that there is no nonzero vector x in Rn such that Ax = x. Show that A - In is nonsingular.
Prove or find a counterexample to disprove each of the following: (a) rank(A + B) ( max{rank A, rank B} (b) rank(A + B) ( min{rank A, rank B} (c) rank(A + B) = rank A + rank B
How can sensitivity analysis help in appraising capital investments? What are the limitations of sensitivity analysis?
21 West Coast Tours runs boat tours along the west coast of British Columbia. On March 5, 2023, it purchased, with cash, a cruising boat for $936,000, having a useful life of 10 years or 13,800...
02 P4-3B. Multi-step Income Statement The adjusted trial balance of Patton Corporation on December 31 is shown below. PATTON CORPORATION Adjusted Trial Balance December 31 Debit Credit Cash.......
What is the relevance of shareholder value-chain activities in consideration of the acquisition of a related business diversification? Be descriptive and expansive in your response
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 600 hours of production time available in its cutting and sewing...
Required information Use the following information for the Exercises 8-10 below. (Algo) [The following information applies to the questions displayed below.] Hemming Company reported the following...
Consider two insulating balls with evenly distributed equal and opposite charges on their surfaces, held with a certain distance between the centers of the balls. Construct a problem in which you...
All of the following assets can be depreciated, except: (a) A bulldozer (b) A copper mine (c) A surgical robot (d) A conveyor belt
In each part, use the given information to find the real numbers x and y. (x + y) + (x - y)i = 3 + i
In each part, solve for z. (a) z + (1 - i ) = 3 + 2i (b) (i - z) + (2z - 3i) = - 2 + 7i
In each part, find z1z2, z12, and z22 (a) z1 = 3i, z2 = 1 - i (b) z1 = 4 + 6i, z2 = 2 - 3i (c) z1 = 1/3 (2 + 4i), z2 = 1/2 (1 - 5i)
1-The yield to maturity will be greater than the coupon rate when a bond is selling at a premium. Select one: a. False b. True 2-Which one of the following would have the greatest present value,...
! Required information [ The following information applies to the questions displayed below. ] Year 1 total cash dividends Year 2 total cash dividends Year 3 total cash dividends Year 4 total cash...
WISE-HOLLAND CORPORATION On June 15, 2013, Marianne Wise and Dory Holland came to your office for an initial meeting. The primary purpose of the meeting was to discuss Wise-Holland Corporation's tax...

Let A be an m ( n matrix. Prove that if AT A is nonsingular, then rank

Question:

Step by Step Answer:

Assume rank A n Then the columns of A are linearly dependent Hence ther...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions