Let a, b,7 e R* be three nonzero vectors and {a, b} be a linearly independent set. Then which of the following is always correct? 1. If BE (7, 7), then the set {7 + B,a +, - +2} is linearly independent. II. If 7 a, b), then the set {a, b, 7} is linearly independent. III. If a ¢ (6,7), then the set {a, B,7} spans R5. IV. For all * e R, E(7,B). (a) Only I (b) Only III (c) Only II (d) Only II and IV (e) Only I, III and IV

Let a, b,7 e R* be three nonzero vectors and {a, b} be a linearly independent set. Then which of the following is always correct? 1. If BE (7, 7), then the set {7 + B,a +, - +2} is linearly independent. II. If 7 a, b), then the set {a, b, 7} is linearly independent. III. If a ¢ (6,7), then the set {a, B,7} spans R5. IV. For all * e R, E(7,B). (a) Only I (b) Only III (c) Only II (d) Only II and IV (e) Only I, III and IV

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let a, b,7 e R* be three nonzero vectors and {a, b} be a linearly independent set. Then which
of the following is always correct?
1. If BE (7, 7), then the set {7 + B,a +, - +2} is linearly independent.
II. If 7
a, b), then the set {a, b, 7} is linearly independent.
III. If a ¢ (6,7), then the set {a,B,7} spans R5.
IV. For all 3 E R, E(7,B).
(a) Only I
(b) Only III
(c) Only II
(d) Only II and IV
(e) Only I, III and IV

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