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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
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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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).
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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