(c) Which of the following statements are FALSE? (1) Let A E Mnxn(F). If (A1, v1) and (A2, v2) are eigenpairs of A, then (A1, v1 + v2) is an eigenpair of A. (2) Let A € Mnxn(F). If A is diagonalizable, then there exist an invertible matrix P and a unique diagonal matrix D such that P-AP = D. (3) Let T = {v1, V2, ..., V,} € F" and let w € F". If T is linearly independent, then TU{w} is linearly dependent. Answer for (c): (d) Which of the following statements are FALSE? 2+3i 4 - 5i (1) If C = then Cx = 0 has only the trivial solution. 2- 3і —3— 21, (2) Every subset of a vector space V that contains the zero vector in V is a subspace of V. (3) If V is a non-trivial subspace of F" and B is a basis for F", then it is possible to reduce B to obtain a basis for V. Answer for (d):
(c) Which of the following statements are FALSE? (1) Let A E Mnxn(F). If (A1, v1) and (A2, v2) are eigenpairs of A, then (A1, v1 + v2) is an eigenpair of A. (2) Let A € Mnxn(F). If A is diagonalizable, then there exist an invertible matrix P and a unique diagonal matrix D such that P-AP = D. (3) Let T = {v1, V2, ..., V,} € F" and let w € F". If T is linearly independent, then TU{w} is linearly dependent. Answer for (c): (d) Which of the following statements are FALSE? 2+3i 4 - 5i (1) If C = then Cx = 0 has only the trivial solution. 2- 3і —3— 21, (2) Every subset of a vector space V that contains the zero vector in V is a subspace of V. (3) If V is a non-trivial subspace of F" and B is a basis for F", then it is possible to reduce B to obtain a basis for V. Answer for (d):
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(c) Which of the following statements are FALSE?
(1) Let A E Mnxn(F).
If (A1, v1) and (A2, v2) are eigenpairs of A, then (A1, V1 + v2) is an eigenpair of A.
(2) Let A € Mnxn(F). If A is diagonalizable, then there exist an invertible matrix P and
a unique diagonal matrix D such that P-AP = D.
(3) Let T = {v1, V2, ..., V,} € F" and let w € F".
If T is linearly independent, then TU{w} is linearly dependent.
Answer for (c):
(d) Which of the following statements are FALSE?
2+3i
4 – 5i
(1) If C =
then Cx = 0 has only the trivial solution.
2 - Зі —3— 2і,
(2) Every subset of a vector space V that contains the zero vector in V is a subspace of V.
(3) If V is a non-trivial subspace of F" and B is a basis for F", then it is possible to reduce B
to obtain a basis for V.
Answer for (d):
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