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For the following matrices find their rank and null-space 3 2 1 (a) A = 0 1 2 020 1 -2 1 3 (b) A -3 6 -3-9 4 -8 4 12 Determine all vectors v orthogonal to (a) u = (1,1,0) (b) u = (5,-6) find the measure of the angle between the vectors u and v. (a) u = (3,1,2) v = (1, −1, −2) (b) u = (1,1,0) v = (0, 1, −1)

For the following matrices find their rank and null-space 3 2 1 (a) A = 0 1 2 020 1 -2 1 3 (b) A -3 6 -3-9 4 -8 4 12 Determine all vectors v orthogonal to (a) u = (1,1,0) (b) u = (5,-6) find the measure of the angle between the vectors u and v. (a) u = (3,1,2) v = (1, −1, −2) (b) u = (1,1,0) v = (0, 1, −1)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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For the following matrices find their rank and null-space 3 2 1 (a) A = 0 1 2 020 1 -2 1 3 (b) A -3 6 -3-9 4 -8 4 12 Determine all vectors v orthogonal to (a) u = (1,1,0) (b) u = (5,-6) find the measure of the angle between the vectors u and v. (a) u = (3,1,2) v = (1, −1, −2) (b) u = (1,1,0) v = (0, 1, −1)
Transcribed Image Text:For the following matrices find their rank and null-space 3 2 1 (a) A = 0 1 2 020 1 -2 1 3 (b) A -3 6 -3-9 4 -8 4 12 Determine all vectors v orthogonal to (a) u = (1,1,0) (b) u = (5,-6) find the measure of the angle between the vectors u and v. (a) u = (3,1,2) v = (1, −1, −2) (b) u = (1,1,0) v = (0, 1, −1)
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