1. Consider the following four vectors in R5. V₁ = Let U span {V₁, V2, V3, V4}. = 0 2, 0 V3 2 0 V₁ II For the purposes of this exercise (and only this one), if you need to row-reduce a matrix, you can have a computer do it and just write down the RREF, as long as you mention the resource(s) you used. (a) Let 6= [4 5 8 0 -7]. Determine whether be U. Explain your reasoning. E (b) Determine whether e₁ EU. Explain your reasoning. (c) Find a 5 × 3 matrix A such that im(A) = U, and explain how you know your choice works. Hint. For this and the next part, you may find the result you proved in Written Assignment 1 useful. (d) Find a 5 × 5 matrix B, which has no columns of all zeroes, such that im(B) = U, and explain how you know your choice works.
1. Consider the following four vectors in R5. V₁ = Let U span {V₁, V2, V3, V4}. = 0 2, 0 V3 2 0 V₁ II For the purposes of this exercise (and only this one), if you need to row-reduce a matrix, you can have a computer do it and just write down the RREF, as long as you mention the resource(s) you used. (a) Let 6= [4 5 8 0 -7]. Determine whether be U. Explain your reasoning. E (b) Determine whether e₁ EU. Explain your reasoning. (c) Find a 5 × 3 matrix A such that im(A) = U, and explain how you know your choice works. Hint. For this and the next part, you may find the result you proved in Written Assignment 1 useful. (d) Find a 5 × 5 matrix B, which has no columns of all zeroes, such that im(B) = U, and explain how you know your choice works.
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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I am really stuck on this question, can you explain your argument
![1. Consider the following four vectors in R5.
V₁ =
0
2
V3
2
0
3
V4
Let U = span {1, V2, V3, V4}.
For the purposes of this exercise (and only this one), if you need to row-reduce a matrix, you can have a
computer do it and just write down the RREF, as long as you mention the resource(s) you used.
(a) Let 6= [4 5 8 0 -7]. Determine whether EU. Explain your reasoning.
(b) Determine whether e₁ EU. Explain your reasoning.
(c) Find a 5 x 3 matrix A such that im(A) = U, and explain how you know your choice works.
Hint. For this and the next part, you may find the result you proved in Written Assignment 1 useful.
(d) Find a 5 × 5 matrix B, which has no columns of all zeroes, such that im(B) = U, and explain how you
know your choice works.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a487e32-6445-4eef-9c62-953e844751ce%2Fbee9e5a8-fd8d-4846-936f-1add5af1e1e9%2Fzzuneq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the following four vectors in R5.
V₁ =
0
2
V3
2
0
3
V4
Let U = span {1, V2, V3, V4}.
For the purposes of this exercise (and only this one), if you need to row-reduce a matrix, you can have a
computer do it and just write down the RREF, as long as you mention the resource(s) you used.
(a) Let 6= [4 5 8 0 -7]. Determine whether EU. Explain your reasoning.
(b) Determine whether e₁ EU. Explain your reasoning.
(c) Find a 5 x 3 matrix A such that im(A) = U, and explain how you know your choice works.
Hint. For this and the next part, you may find the result you proved in Written Assignment 1 useful.
(d) Find a 5 × 5 matrix B, which has no columns of all zeroes, such that im(B) = U, and explain how you
know your choice works.
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