Let a₁ = 1 5 -1 a₂ -6 - 25 3 and b = 3 -5 . For what value(s) of h is b in the plane spanned by a, and a₂? h The value(s) of h is(are). (Use a comma to separate answers as needed.)

Linear Algebra: A Modern Introduction
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Chapter1: Vectors
Section1.3: Lines And Planes
Problem 42EQ
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Let a₁ =
1
5
-1
№
The value(s) of h is(are)
- 6
- 25
3
and b =
3
-5
. For what value(s) of h is b in the plane spanned by a₁ and a2?
h
(Use a comma to separate answers as needed.)
Transcribed Image Text:Let a₁ = 1 5 -1 № The value(s) of h is(are) - 6 - 25 3 and b = 3 -5 . For what value(s) of h is b in the plane spanned by a₁ and a2? h (Use a comma to separate answers as needed.)
Let A =
1 0 -6
03-5
-59 4
and b =
9
-2. Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a2, ª3}.
- 29
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. No, b is not in (a₁, a2, aç} since b is not equal to a₁, a2, or a3.
B. Yes, b is in (a₁, a2, a3} since b = a
(Type a whole number.)
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 = (a₁ + a₂ + ([ аз.
(Simplify your answers.)
D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, №₂, and аз.
Transcribed Image Text:Let A = 1 0 -6 03-5 -59 4 and b = 9 -2. Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a2, ª3}. - 29 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. No, b is not in (a₁, a2, aç} since b is not equal to a₁, a2, or a3. B. Yes, b is in (a₁, a2, a3} since b = a (Type a whole number.) 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 = (a₁ + a₂ + ([ аз. (Simplify your answers.) D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, №₂, and аз.
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