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.]
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.]
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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![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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F324f16c4-c4e5-4b06-b074-f261b39e021a%2F23569460-f09b-4338-8be1-4235e962ec7e%2Fgi56ejn_processed.png&w=3840&q=75)
Transcribed Image Text: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.]
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