Let [v1, v2,...,vn} be a basis of Rn (written as columns), and let A be an n

Question:

Let [v1, v2,...,vn} be a basis of Rn (written as columns), and let A be an n × n matrix.
If {Av1, Av2,..., Ayn} is a basis of Rn, show that A is invertible.

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 06:44 AM

See More Questions

Suppose A is an m n matrix. (a) Let v1,..., vn be a basis of Rn, and Av1 = w1 Rm, for i = 1........n. Prove that the vectors v1,..., vn, w1,..., wn, serve to uniquely specify A. (b) Write down a...
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.
Let v1,..., vn be a basis for Rn. (a) Show that any affine function F[x] = Ax + b on Rn is uniquely determined by the n + 1 vectors w0 = F[0], w1 = F[v1],..., wn = F[vn]. (b) Find the formula for A...
Two wires carrying equal and opposite currents are twisted together in the construction of a circuit. Why does this technique reduce stray magnetic fields? Please explain for dummies.
The following comments summarize the beliefs of some practitioners about the Sarbanes-Oxley Act and the PCAOB. The Sarbanes-Oxley Act is unnecessary regulation of the profession. The costs of...
What is an interbank transfer schedule, and why is it needed?
A single acting reciprocating pump has to deliver water against a total head of 50 m. The plunger diameter is 120 mm. What is the force exerted by the plunger during delivery stroke? Assume pump...
Journal entries for prepaid rent ABB Group (ABB), headquartered in Switzerland, is one of the worlds largest engineering companies. ABB applies U.S. GAAP, and reports its results in millions of U.S,...
In organizational behavior, understanding the factors that predict organizational performance is crucial for managers and researchers. Numerous theories and studies have attempted to shed light on...
An experiment was conducted to test the efficacy of chloromycetin in checking typhoid. In a certain hospital chloromycetin was given to 285 out of the 392 patients suffering from typhoid. The number...
As a pendulum swings (see the diagram), let t measure the time since it was vertical. The angle Î¸ = Î¸(t) from the vertical can be shown to satisfy the equation...
Show that null A = null(AT A) for any real matrix A.
Draw the shear and bending-moment diagrams for the beam AB, and determine the maximum absolute values of the shear and bending moment. 250 mina 200 mm 100 mm 4KIN 200 N 200 N 250 mm 150 mm 150 mm 250...
State the objectives of audit of government accounts and compare them with those of the audit under the Companies Act.
Mention important items for which auditor would refer to each of the following: (a) Minutes book of the Board Meeting (b) Minutes book of the Shareholders Meeting.
What is a clean report? Give a specimen of a clean report of the auditor.
Discuss the different stages of conducting bank audit.
What do you mean by the term computer-assisted audit techniques? State the factors to be considered before using these techniques.
Mate Ease is an Internet dating service. All members pay in advance to be listed in the database. Advance payments are credited to an account entitled Unearned Member Dues. Adjusting entries are...
If someone's Z-score for a variable was 0.67. Their score is a significant extreme score. Their score is not significant. O Their score is slightly above average. O Their score is an outlier.
If p is a nonnegative integer and c is a scalar, show that (cA)P = cpAp.
For a square matrix A and a nonnegative integer p, show that (AT)P = (AP)T.
For a nonsingular matrix A and a nonnegative integer p, show that (AP)-1 = (A-1)P.
A steel cable that weighs 8 lb/ft is used to pull a 500 lb block of concrete from the ground to the top of a 120 ft tall building. Let x be the distance, in feet, from the block to the TOP of the...
Three metal fishing weights, each with a mass of 1.00102 g and at a temperature of 100.0C, are placed in 1.00102 g of water at 35.0C. The final temperature of the mixture is 45.0C. What is the...
A useful quantitative model for the grinding of lenses with known focal lengths is the lens-makers' equation: nlens environment 1) (1/4-1/2), where f is the focal length of the lens, the two index of...

Let [v1, v2,...,vn} be a basis of Rn (written as columns), and let A be an n

Question:

Step by Step Answer:

Suppose Ax 1 Ax n is a basis of R n To show that A is ...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions