1. Consider the following four vectors in R5. V₁ = 0 2 V3 2 0 3 V4 Let U span {1, U2, U3, U4}. 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 x 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 = 0 2 V3 2 0 3 V4 Let U span {1, U2, U3, U4}. 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 x 5 matrix B, which has no columns of all zeroes, such that im(B) = U, and explain how you know your choice works.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 17EQ
Related questions
Question
![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%2F969a5512-adf8-47e2-98fb-7969e90a209a%2Fp3urfem_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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