Let A = 10-6 11 0 3-4 and b= -1 Denote the columns of A by a₁, a2, a3, and let W= Span (a₁, az, a3). -39 2 - 28 a. Is b in (a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] C a. Is b in (a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. Yes, b is in (a₁, a₂, a3} since b=a (Type a whole number.) OB. No, b is not in (a₁, a2, a3} since b is not equal to a₁, a2, or a3. O C. Yes, bis in (a₁, 22, 23) since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear combination of them. In particular, b = (Simplify your answers.) O D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3.
Let A = 10-6 11 0 3-4 and b= -1 Denote the columns of A by a₁, a2, a3, and let W= Span (a₁, az, a3). -39 2 - 28 a. Is b in (a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] C a. Is b in (a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. Yes, b is in (a₁, a₂, a3} since b=a (Type a whole number.) OB. No, b is not in (a₁, a2, a3} since b is not equal to a₁, a2, or a3. O C. Yes, bis in (a₁, 22, 23) since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear combination of them. In particular, b = (Simplify your answers.) O D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3.
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
![Let A =
10 - 6
03 - 4 and b =
-39 2
11
- 1
- 28
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}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a. Is b in {a₁, a₂, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A.
Yes, b is in {a₁, a2, a3} since b=a
(Type a whole number.)
B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a₁, a2, a3} since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b =
(Simplify your answers.)
аз.
D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and
) a₁ + a₂ + ( ) a3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a6c3af6-91f1-478b-99db-a0b0fd9518f2%2Ff55cf825-6b6f-401b-9992-94ecc0bd09bb%2Fprod64t_processed.png&w=3840&q=75)
Transcribed Image Text:Let A =
10 - 6
03 - 4 and b =
-39 2
11
- 1
- 28
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}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a. Is b in {a₁, a₂, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A.
Yes, b is in {a₁, a2, a3} since b=a
(Type a whole number.)
B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a₁, a2, a3} since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b =
(Simplify your answers.)
аз.
D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and
) a₁ + a₂ + ( ) a3.
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