Let A = 10-3 0 22 and b = - 4 4 2 -1 6 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. 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.) O C. Yes, b is in W since ba (Type a whole number.) B. No, b is not in (a₁, a2, a3} since b is not equal to a₁, a2, or a3. O C. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3. OD. Yes, b is in (a₁, a2, a3} since b = a (Type a whole per.) 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. A. There is(are) 3 vector(s) in (a₁, a2, a3}. (Type a whole number.) OB. There are infinitely many vectors in (a₁, a₂, a3}. 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. B. No, b is not in W since it cannot be generated by a linear combination of a₁, a2, and a3. · ( ) a₁ + ( ) a₂ + ( )az.
Let A = 10-3 0 22 and b = - 4 4 2 -1 6 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. 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.) O C. Yes, b is in W since ba (Type a whole number.) B. No, b is not in (a₁, a2, a3} since b is not equal to a₁, a2, or a3. O C. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3. OD. Yes, b is in (a₁, a2, a3} since b = a (Type a whole per.) 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. A. There is(are) 3 vector(s) in (a₁, a2, a3}. (Type a whole number.) OB. There are infinitely many vectors in (a₁, a₂, a3}. 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. B. No, b is not in W since it cannot be generated by a linear combination of a₁, a2, and a3. · ( ) a₁ + ( ) a₂ + ( )az.
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
What is the answer for b)
Explain in detail please
c)Please do c as well
Transcribed Image Text: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. No, b is not in W since b is not equal to a₁, a2, or a3.
B. No, b is not in W since it cannot be generated by a linear combination of a₁, a₂,
and
OC. 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 =
(Simplify your answers.)
a3.
1) a₁ + a₂ + (a3.
![Let A =
10 - 3
02 -2 and b=
- 4 4 2
-1
- 2 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a2, a3}.
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.]
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, 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.)
B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3.
C. No, b is not in (a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3.
D. Yes, b is in {a₁, a2, a3} since b = a
(Type a whole number.)
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.
A. There is(are) 3 vector(s) in {a₁, a₂, a3}.
(Type a whole number.)
B. There are infinitely many vectors in {a₁, ª2, ª3}.
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. No, b is not in W since b is not equal to a₁, a2, or a3.
B. No, b is not in W since it cannot be generated by a linear combination of a₁, a2, and аз.
O C. Yes, b is in W since b=a
(Type a whole number.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbea0901b-9b71-43dc-90d5-d9e10ed3de89%2Ff3269aca-f3f4-42ba-beca-946edd6a85b7%2Focfr8jr_processed.png&w=3840&q=75)
Transcribed Image Text:Let A =
10 - 3
02 -2 and b=
- 4 4 2
-1
- 2 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a2, a3}.
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.]
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, 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.)
B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3.
C. No, b is not in (a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and a3.
D. Yes, b is in {a₁, a2, a3} since b = a
(Type a whole number.)
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.
A. There is(are) 3 vector(s) in {a₁, a₂, a3}.
(Type a whole number.)
B. There are infinitely many vectors in {a₁, ª2, ª3}.
b. Is b in W? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. No, b is not in W since b is not equal to a₁, a2, or a3.
B. No, b is not in W since it cannot be generated by a linear combination of a₁, a2, and аз.
O C. Yes, b is in W since b=a
(Type a whole number.)
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