Let A = 10-2 04-6 and b= 0 22 Denote the columns of A by a₁. a2 a3. and let W = Span (a₁. ₂. 3) -48 6 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 = 10-2 04-6 and b= 0 22 Denote the columns of A by a₁. a2 a3. and let W = Span (a₁. ₂. 3) -48 6 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
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Please do last part
![Let A =
10-2
04-6
- 6 and b=
-48 6
0
599
-6. Denote the columns of A by a₁. a2. a3. and let W = Span (a₁. az.ªz).
- 22
a. Is b in (a₁, a2 a3)? How many vectors are in (a₁ a2 a3)?
1
b. Is b in W? How many vectors are in W?
c. Show that a₂ is in W. [Hint: Row operations are unnecessary.]
Yes, b is in (a₁ a2 a3) since b = a
(Type a whole number.)
No. b is not in (a₁, a2, a3) since it cannot be generated by a linear combination of a₁, a₂, and a3.
Yes, b is in (a₁, az, 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+ ( )az.
(Simplify your answers.)
No. b is not in (a₁ a2 a3) since b is not equal to a₁, a2, or a3.
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.
There is (are) 3 vector(s) in (a₁ a₂ a3).
(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.
ⒸA. 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.)
OB. Yes, b is in W since b = a
(Type a whole number.)
OC. No, b is not in W since it cannot be generated by a linear combination of a₁ a₂, and a.
OD. 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%2Ffc7deb2c-0862-415e-88b2-023e0d274874%2Fcb51c3c2-a108-4097-bf28-352755fc0e23%2Fpxbo6r8_processed.png&w=3840&q=75)
Transcribed Image Text:Let A =
10-2
04-6
- 6 and b=
-48 6
0
599
-6. Denote the columns of A by a₁. a2. a3. and let W = Span (a₁. az.ªz).
- 22
a. Is b in (a₁, a2 a3)? How many vectors are in (a₁ a2 a3)?
1
b. Is b in W? How many vectors are in W?
c. Show that a₂ is in W. [Hint: Row operations are unnecessary.]
Yes, b is in (a₁ a2 a3) since b = a
(Type a whole number.)
No. b is not in (a₁, a2, a3) since it cannot be generated by a linear combination of a₁, a₂, and a3.
Yes, b is in (a₁, az, 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+ ( )az.
(Simplify your answers.)
No. b is not in (a₁ a2 a3) since b is not equal to a₁, a2, or a3.
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.
There is (are) 3 vector(s) in (a₁ a₂ a3).
(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.
ⒸA. 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.)
OB. Yes, b is in W since b = a
(Type a whole number.)
OC. No, b is not in W since it cannot be generated by a linear combination of a₁ a₂, and a.
OD. No. b is not in W since b is not equal to a₁ a₂ or a3
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