Let A =10-21026 and b =4Denote the columns of A by a₁, a2, a3, and let-6 4 4-6W = Span {a1, a2, 3}-a. Is b in {a̸₁, a₂, a̸3}? How many vectors are in {a₁, a₂, a3}?b. Is b in W? How many vectors are in W?c. Show that a₁ is in W. [Hint: Row operations are unnecessary.]

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Answered: Let A = 10-2 1 026 and b = 4 Denote the…

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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If A = [a1, a2, a3] has as columns the three vectors a1, a2, and a3. What is y = Ax,where x is a vector with three components, x1, x2, x3? Is y in the column spaceof A?
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Let A = 10-2 1 026 and b = 4 Denote the columns of A by a₁, a2, a3, and let -6 4 4 -6 W = Span {a1, a2, 3}- a. Is b in {a̸₁, a₂, a̸3}? How many vectors are in {a₁, a₂, a3}? b. Is b in W? How many vectors are in W? c. Show that a₁ is in W. [Hint: Row operations are unnecessary.]