5. For which value of x do the following vectors form a linearly dependent set in ² (글 글) (글 글(글 글)
5. For which value of x do the following vectors form a linearly dependent set in ² (글 글) (글 글(글 글)
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
Please answer no. 5
![03:21 Afternoon Wed, Jun 1A f...
403
1. Let V be the set of all 2 x 2 matrices 4-[]; such that the product abcd = 0 with standard operations on matrices
a. Is V close under addition? Show your proof.
b. Is V close under scalar multiplication? Show your proof.
c. What is the zero vector in V?
d. Does every matrix A in V have
negative that is in V? Explain
e. Is V a vector space? Explain
2. Is the set of vectors of the form
a subspace of R³? Show your proof.
[a+26
3. Show that the vectors =(0, 3, 1, -1); v = (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly dependent set in R¹?
4. Express V₁ in number 3 as linear combination of V₂ and V3.
5. For which value of x do the following vectors form a linearly dependent set in R³
n=(x, &• in-( * )=( )
x₂
■
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2ade466-87ff-48da-ae6a-268545b860cb%2F3303bef4-2608-4266-a8e6-3e0ce7bd1a11%2Fr5umwjj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:03:21 Afternoon Wed, Jun 1A f...
403
1. Let V be the set of all 2 x 2 matrices 4-[]; such that the product abcd = 0 with standard operations on matrices
a. Is V close under addition? Show your proof.
b. Is V close under scalar multiplication? Show your proof.
c. What is the zero vector in V?
d. Does every matrix A in V have
negative that is in V? Explain
e. Is V a vector space? Explain
2. Is the set of vectors of the form
a subspace of R³? Show your proof.
[a+26
3. Show that the vectors =(0, 3, 1, -1); v = (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly dependent set in R¹?
4. Express V₁ in number 3 as linear combination of V₂ and V3.
5. For which value of x do the following vectors form a linearly dependent set in R³
n=(x, &• in-( * )=( )
x₂
■
O
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