3. Let A be the matrix given below. We also are given R, its reduced row echelon and let w be a vector in R*. Г1 о 01 0 1 -3 0 [1 2 -2 1] 4 8. 2 5 A = 2 1 5 2 |-6 R = k [з 2 6 Lo o a. Give bases for col(A),row(A) and null(A). b. Find the value of k such that w" is in row(A). Give the coordinate vector with respect to the basis found in a). c. Find the value of k such that w is in null(A). Give the coordinate vector with respect to the basis found in a). d. Verify the statement from #2: the vector found in row(A) is orthogonal to the one in null(A).
3. Let A be the matrix given below. We also are given R, its reduced row echelon and let w be a vector in R*. Г1 о 01 0 1 -3 0 [1 2 -2 1] 4 8. 2 5 A = 2 1 5 2 |-6 R = k [з 2 6 Lo o a. Give bases for col(A),row(A) and null(A). b. Find the value of k such that w" is in row(A). Give the coordinate vector with respect to the basis found in a). c. Find the value of k such that w is in null(A). Give the coordinate vector with respect to the basis found in a). d. Verify the statement from #2: the vector found in row(A) is orthogonal to the one in null(A).
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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Question
![3. Let A be the matrix given below. We also are given R, its reduced row echelon and let w
be a vector in R*.
Г1 о
01
0 1 -3 0
[1 2 -2 1]
4
8.
2 5
A =
2 1
5
2
|-6
R =
k
[з 2 6
Lo o
a. Give bases for col(A),row(A) and null(A).
b. Find the value of k such that w" is in row(A). Give the coordinate vector with
respect to the basis found in a).
c. Find the value of k such that w is in null(A). Give the coordinate vector with
respect to the basis found in a).
d. Verify the statement from #2: the vector found in row(A) is orthogonal to the
one in null(A).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F161beadb-85e0-4933-a3f5-87930572fea5%2F3dba7ef4-5612-4f2f-8da9-122c0d7bdcfb%2Fjaxyyw.png&w=3840&q=75)
Transcribed Image Text:3. Let A be the matrix given below. We also are given R, its reduced row echelon and let w
be a vector in R*.
Г1 о
01
0 1 -3 0
[1 2 -2 1]
4
8.
2 5
A =
2 1
5
2
|-6
R =
k
[з 2 6
Lo o
a. Give bases for col(A),row(A) and null(A).
b. Find the value of k such that w" is in row(A). Give the coordinate vector with
respect to the basis found in a).
c. Find the value of k such that w is in null(A). Give the coordinate vector with
respect to the basis found in a).
d. Verify the statement from #2: the vector found in row(A) is orthogonal to the
one in null(A).
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