Let A= 10-6 04-3 and b= -48 22 8 Denote the columns of A by a₁, a2, a3, and let W=Span (a₁, a2, a3). -16 a. Is b in (a₁, a2, a3})? How many vectors are in (a₁, 82, 83}? b. Is b in W? How many vectors are in W? c. Show that a, 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. OA. Yes, bis 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 = (a₁ + a₂ + (ª3. (Simplify your answers.) OB. No, b is not in (a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3. ⒸC. Yes, b is in (a₁. a2, a3} since b = a (Type a whole number.) OD. No, b is not in (a₁. a2, a3) since b is not equal to a₁, 8₂, or a3.
Let A= 10-6 04-3 and b= -48 22 8 Denote the columns of A by a₁, a2, a3, and let W=Span (a₁, a2, a3). -16 a. Is b in (a₁, a2, a3})? How many vectors are in (a₁, 82, 83}? b. Is b in W? How many vectors are in W? c. Show that a, 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. OA. Yes, bis 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 = (a₁ + a₂ + (ª3. (Simplify your answers.) OB. No, b is not in (a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3. ⒸC. Yes, b is in (a₁. a2, a3} since b = a (Type a whole number.) OD. No, b is not in (a₁. a2, a3) since b is not equal to a₁, 8₂, or 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
Subject-advance maths
![Let A =
22
13
and b=
- 16
10-6
04-3
-48
8 Denote the columns of A by a₁, a2, a3, and let W = Span (a₁, 8₂, 83).
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.
C
O A. 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.)
OB. No, b is not in (a₁. a2, a3} since t cannot be generated by a linear combination of a₁, a2, and a3.
ⒸC. Yes, b is in (a₁, 82, a3) since b=a
(Type a whole number.)
O D. No, b is not in (a₁, a2, a3) since
is not equal to a₁. a₂, or a3.
a₁ + a₂ + ( ª3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7373726-0d35-46ca-aa27-97bcf9126f3a%2F84c85c9d-77c6-4f28-8660-8eb720629bf1%2Fx0bk42_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let A =
22
13
and b=
- 16
10-6
04-3
-48
8 Denote the columns of A by a₁, a2, a3, and let W = Span (a₁, 8₂, 83).
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.
C
O A. 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.)
OB. No, b is not in (a₁. a2, a3} since t cannot be generated by a linear combination of a₁, a2, and a3.
ⒸC. Yes, b is in (a₁, 82, a3) since b=a
(Type a whole number.)
O D. No, b is not in (a₁, a2, a3) since
is not equal to a₁. a₂, or a3.
a₁ + a₂ + ( ª3.
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