A and B are n x n matrices Check the true statements below:OA. det A™OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, az.C. If one multiple of one row of A is added to another row, the eigenvalues do not change.D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k.(-1)det A.

Answered: Image /qna-images/answer/3a2a56cc-b5f5-4d67-82ad-ce78f27515cc.jpg

Check the true statements below: OA. det AT = (-1)detA. OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, a3. OC. If one multiple of one row of A is added to another row, the eigenvalues do not change. D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k. %3D

Check the true statements below: OA. det AT = (-1)detA. OB. If A is 3x3, with columns a1, a2, a3, then det A equals the volume of the parallelpiped determined by the vectors a1, a2, a3. OC. If one multiple of one row of A is added to another row, the eigenvalues do not change. D. If (A – r)k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k. %3D

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

See similar textbooks