Let A = 10-6 04-2 and 14 -2. Denote the columns of A by a₁. 2. 3. and let W=Span (a₁ a2. a3). -13 -38 3 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 a, is in W. [Hint: Row operations are unnecessary.]
Let A = 10-6 04-2 and 14 -2. Denote the columns of A by a₁. 2. 3. and let W=Span (a₁ a2. a3). -13 -38 3 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 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
![Let A =
10 -6
0 42 and b =
-38 3
14
- 2
- 13
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 a, 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.
Yes, bis in (a₁, az, aç} since, although b is not equal to a₁. az, or a3, it can be expressed as a linear combination of them. In particular, b = ( )a₁ + ( )a₂+ ( )az.
1
(Simplify your answers.)
Yes, b is in (a₁, 82, 83) since b = a
1
(Type a whole number.)
No. b is not in (a₁, az, a3, since it cannot be generated by a linear combination of a₁, a₂, and a3.
No. b is not in (a₁, a2 a3 since b is not equal to a₁, a2, or a3.
C
How many vectors are in (a₁ a2 a3)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
1
There is (are) 3 vector(s) in (a₁ a₂ a3).
1
(Type a whole number.)
There are infinitely many vectors in (a₁. a2. a3).
1:
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. No, b is not in W since b is not equal to a₁, a₂, or a3.
OB. No, b is not in W since it cannot be generated by a linear combination of a₁, a. and a.
1
O C. Yes, b is in W since b=a
(Type a whole number.)
ⒸD. Yes, b is in W since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b = (-2) a₁ + ( − 4) a₂ + ( − 1) ªz.
(Simplify your answers.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc7deb2c-0862-415e-88b2-023e0d274874%2F9eee5c62-2f5f-424e-80e5-4084ddf4f0a1%2Fvzvbj7c_processed.png&w=3840&q=75)
Transcribed Image Text:Let A =
10 -6
0 42 and b =
-38 3
14
- 2
- 13
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 a, 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.
Yes, bis in (a₁, az, aç} since, although b is not equal to a₁. az, or a3, it can be expressed as a linear combination of them. In particular, b = ( )a₁ + ( )a₂+ ( )az.
1
(Simplify your answers.)
Yes, b is in (a₁, 82, 83) since b = a
1
(Type a whole number.)
No. b is not in (a₁, az, a3, since it cannot be generated by a linear combination of a₁, a₂, and a3.
No. b is not in (a₁, a2 a3 since b is not equal to a₁, a2, or a3.
C
How many vectors are in (a₁ a2 a3)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
1
There is (are) 3 vector(s) in (a₁ a₂ a3).
1
(Type a whole number.)
There are infinitely many vectors in (a₁. a2. a3).
1:
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. No, b is not in W since b is not equal to a₁, a₂, or a3.
OB. No, b is not in W since it cannot be generated by a linear combination of a₁, a. and a.
1
O C. Yes, b is in W since b=a
(Type a whole number.)
ⒸD. Yes, b is in W since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b = (-2) a₁ + ( − 4) a₂ + ( − 1) ªz.
(Simplify your answers.)
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