you make and explain how do you know tha is a
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
Solve #5 prove the proble show every step you make and explain how do you know tha is a subspace. POST PICTURTES OF YOUR WORK
![Discussion Questions
1. Let B=
Let 8-CO-ED
justify your answer.
3 show that B is a basis for R³ and determine [v]B for 2
H
2. What does it mean for a group of statements to be equivalent? How does that apply to the
Invertible Matrix Theorem?
3. Suppose that A=
[1
1
3
2 31
5 5
2
[1 0 11
1 1
00
2
0
What is a geometric interpretation of the span of the column vectors of A? Confirm the Rank-
Nullity Theorem.
-1
3
and rrefA
Make sure you
=
0
0
. Find Nullspace(A) and Colspace(A).
4. Confirm that 5-3x+x², 7-3x+2x², 4+3x is a basis for P₂(R). Find 8+3x-7x² in the new basis.
5. Suppose that nullspace (A)=0, explain how this tells us that the column vectors of A are linearly
independent. Remember that A is not necessarily square.
6. Suppose that A is a square n x n matrix with coefficients in R and colspace(A) is not R", explain
how you know that A is not invertible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2F981cc95b-ebf3-4059-a8e7-4b453963cb99%2Fu5j9dd_processed.png&w=3840&q=75)
Transcribed Image Text:Discussion Questions
1. Let B=
Let 8-CO-ED
justify your answer.
3 show that B is a basis for R³ and determine [v]B for 2
H
2. What does it mean for a group of statements to be equivalent? How does that apply to the
Invertible Matrix Theorem?
3. Suppose that A=
[1
1
3
2 31
5 5
2
[1 0 11
1 1
00
2
0
What is a geometric interpretation of the span of the column vectors of A? Confirm the Rank-
Nullity Theorem.
-1
3
and rrefA
Make sure you
=
0
0
. Find Nullspace(A) and Colspace(A).
4. Confirm that 5-3x+x², 7-3x+2x², 4+3x is a basis for P₂(R). Find 8+3x-7x² in the new basis.
5. Suppose that nullspace (A)=0, explain how this tells us that the column vectors of A are linearly
independent. Remember that A is not necessarily square.
6. Suppose that A is a square n x n matrix with coefficients in R and colspace(A) is not R", explain
how you know that A is not invertible.
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