Let A = 10-2 04-4 -58 4 and b = 4 - 30 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a₂, a3}. a. Is b in {a₁, a₂, a3}? How many vectors are in {a₁, a₂, a3}? 1 b. Is b in W? How many vectors are in W? c. Show that a is in W. [Hint: Row operations are unnecessary.]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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 Is b in​ W? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

Let A =
10-2
0 44 and b =
-58 4
6
4
- 30
Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, ª2, №3}.
? How many vectors are in {a₁, a2,
a. Is b in {a₁, 22,
1
‚ a3}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a3}?
Transcribed Image Text:Let A = 10-2 0 44 and b = -58 4 6 4 - 30 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, ª2, №3}. ? How many vectors are in {a₁, a2, a. Is b in {a₁, 22, 1 ‚ a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a3}?
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