1) S = {a + bx + cx²: a + 2b – 3c = 1; a, b, cE R} 2) S = {a + bx + cx²: a + 2b – 3c = 0; a, b, c E R} 3)
1) S = {a + bx + cx²: a + 2b – 3c = 1; a, b, cE R} 2) S = {a + bx + cx²: a + 2b – 3c = 0; a, b, c E R} 3)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 42CR: Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a...
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please show work as neat and complete as possible.
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![Include every possible detail in the solutions of all problems.
Be sure to check your notation.
Either prove that the given set S is a subspace of the vector space V or demonstrate that S
is not a subspace of V.
In your proofs, do not combine steps.
Any time you rely on a property of real numbers, indicate which property of real numbers
I.
you are using to go from one step to the next.
Do not use linear combinations when proving S is a subspace.
Instead, treat vector addition and scalar multiplication separately, the way we did it in class.
To demonstrate that S is not subspace, show that one of the ten criteria for being a
subspace fails to hold true.
1)
S = {a + bx + cx²: a + 2b – 3c = 1; a, b, c € R}
2)
S %3D {a + bx + сx?: а + 2b — Зс %3D 0%; а, b, с E R}
3)
= {[: "]:« € (-», 0]}
I.
Find a set of vectors S that spans the vector space V.
Begin by parameterizing V; show your work.
r
2r – s
1)
V =
3r + t
: r, s,t E Z
with the usual operations from R°
4r + 6s – t
2)
V =
: 2a – d = 0, -2a + c – 2b + d = 0; a, b, c, d e Z }
with the usual operations from M22](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa9a9ea7-0a60-40f2-88c8-00f846edd995%2F16ba81a1-4acf-4b6e-88ed-806c4154958a%2F129sr6c_processed.png&w=3840&q=75)
Transcribed Image Text:Include every possible detail in the solutions of all problems.
Be sure to check your notation.
Either prove that the given set S is a subspace of the vector space V or demonstrate that S
is not a subspace of V.
In your proofs, do not combine steps.
Any time you rely on a property of real numbers, indicate which property of real numbers
I.
you are using to go from one step to the next.
Do not use linear combinations when proving S is a subspace.
Instead, treat vector addition and scalar multiplication separately, the way we did it in class.
To demonstrate that S is not subspace, show that one of the ten criteria for being a
subspace fails to hold true.
1)
S = {a + bx + cx²: a + 2b – 3c = 1; a, b, c € R}
2)
S %3D {a + bx + сx?: а + 2b — Зс %3D 0%; а, b, с E R}
3)
= {[: "]:« € (-», 0]}
I.
Find a set of vectors S that spans the vector space V.
Begin by parameterizing V; show your work.
r
2r – s
1)
V =
3r + t
: r, s,t E Z
with the usual operations from R°
4r + 6s – t
2)
V =
: 2a – d = 0, -2a + c – 2b + d = 0; a, b, c, d e Z }
with the usual operations from M22
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