10 -2 Let A = 0 3 -4 and b= 5 . Denote the columns of A by a, , a2, a3, and let W = Span {aq, a2, a3}. -46 2 2 a. Is b in fa,, a2, az}? How many vectors are in {a,, a2, ag}? b. Is b in W? How many vectors are in W? c. Show that a, is in W. [Hint: Row operations are unnecessary.]
10 -2 Let A = 0 3 -4 and b= 5 . Denote the columns of A by a, , a2, a3, and let W = Span {aq, a2, a3}. -46 2 2 a. Is b in fa,, a2, az}? How many vectors are in {a,, a2, ag}? 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
Problem 1RQ
Related questions
Question
![1 0
- 2
1
Let A =
0 3
and b =
Denote the columns of A by a,, a2, a3, and let W = Span (a1, a2, a3}.
- 4
%3D
-4 6
2
a. Is b in fa,, a2, az}? How many vectors are in {a1, a2, az}?
|
b. Is b in W? How many vectors are in W?
c. Show that a, is in W. [Hint: Row operations are unnecessary.]
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. Yes, b is in W since, although b is not equal to a,, a2, or a3, it can be expressed as a linear combination of them. In particular,
Da, +
a2 + (
b =
az
(Simplify your answers.)
O B. Yes, b is in W sinceb= a
(Type a whole number.)
O C. No, b is not in W since it cannot be generated by a linear combination of a,, a,,
and
az.
O D. No, b is not in W since b is not equal to a1, a2, or a3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b791583-2ee3-49d0-a0a9-eda79647ecea%2Fa90cace2-6010-4efc-a85c-2002e4827b06%2F88ycibs_processed.png&w=3840&q=75)
Transcribed Image Text:1 0
- 2
1
Let A =
0 3
and b =
Denote the columns of A by a,, a2, a3, and let W = Span (a1, a2, a3}.
- 4
%3D
-4 6
2
a. Is b in fa,, a2, az}? How many vectors are in {a1, a2, az}?
|
b. Is b in W? How many vectors are in W?
c. Show that a, is in W. [Hint: Row operations are unnecessary.]
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. Yes, b is in W since, although b is not equal to a,, a2, or a3, it can be expressed as a linear combination of them. In particular,
Da, +
a2 + (
b =
az
(Simplify your answers.)
O B. Yes, b is in W sinceb= a
(Type a whole number.)
O C. No, b is not in W since it cannot be generated by a linear combination of a,, a,,
and
az.
O D. No, b is not in W since b is not equal to a1, a2, or a3.
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