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(i) Use the projection formula V(V¹V)-¹VT to verify that the orthogonal projection matrix onto the z- 0 0 axis in 3 dimensional space R³ is given by. 0 0 0 1 (ii) Using the first four digits of your code number: a,b,c,d; why is the system of equations: ax + by = 1 cx + dy = 2 (a + c)x+ (b + d)y = 4 obviously inconsistent? Find the least squares solution to this system of equations. (iii) Explain how the theory of orthogonal projections relates to your solution in (ii).

(i) Use the projection formula V(V¹V)-¹VT to verify that the orthogonal projection matrix onto the z- 0 0 axis in 3 dimensional space R³ is given by. 0 0 0 1 (ii) Using the first four digits of your code number: a,b,c,d; why is the system of equations: ax + by = 1 cx + dy = 2 (a + c)x+ (b + d)y = 4 obviously inconsistent? Find the least squares solution to this system of equations. (iii) Explain how the theory of orthogonal projections relates to your solution in (ii).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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A=1 B-2 C=9 D=3

(i) Use the projection formula V(Vª -¹V¹ to verify that the orthogonal projection matrix onto the z- /0 0 0 0 0 0 0 axis in 3 dimensional space R³ is given by. 0 (ii) Using the first four digits of your code number: a,b,c,d; why is the system of equations: ax + by = 1 cx + dy = 2 (a + c)x+ (b + d)y = 4 obviously inconsistent? Find the least squares solution to this system of equations. (iii) Explain how the theory of orthogonal projections relates to your solution in (ii).
Transcribed Image Text:(i) Use the projection formula V(Vª -¹V¹ to verify that the orthogonal projection matrix onto the z- /0 0 0 0 0 0 0 axis in 3 dimensional space R³ is given by. 0 (ii) Using the first four digits of your code number: a,b,c,d; why is the system of equations: ax + by = 1 cx + dy = 2 (a + c)x+ (b + d)y = 4 obviously inconsistent? Find the least squares solution to this system of equations. (iii) Explain how the theory of orthogonal projections relates to your solution in (ii).
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