9. Find a basis for the hyperplane a where a-(2, 1. -3).
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![9. Find a basis for the hyperplane a where a=(2, 1. -3).
10. Suppose that T: R R is a linear transfomation with T(1.0,1) (1,2,0.1).
T(1,1.0)-(2.1,1,0), T(0,1,0)-(1-2,1.1). Find the standard matrix for T.
11. Assume u-(1.0,0,-1), v-(3,2.7,3), vy-(2,1.3.2), and v3-(5,2,9,5).
Show that u is in the orthogonal complement of W=span(v1.V2,V3).
12. Let W be the intersection of the planes 2r-y+z%3D0 and r-2y+2 0 in R3.
Find parametric equations for W-
[26 14]
13. Detemine the rank and nullity of the matrix C=0 1-1
[2 7 13
14. Let W be the subspace of R spanned by the vectors v=(1,0,7). -(6,1,7), and
V3-(14,-1,13). Find bases for W and W-
15. Find the standard matrix for the orthogonal projection of R onto the subspace
spanned by a=(1,1) and a-(0.1).
[10]
16. Find the least squares solution of Ax-b where =01
63=
11
17. Find the least squares straight line fit y ar+b t
the points (2,2). (4,3), and (6.7).
18. Use the Gram-Schmidt process to transform the given basis (W, W, W3} into an
orthogonal basis where wi (1,1,2), w (0,1.1), and w; - (-1,2,1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb59f364d-4f68-4f82-8788-e4b955be2c30%2F20013f67-70b9-4a74-9996-a79b22363786%2F5rmcqhl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9. Find a basis for the hyperplane a where a=(2, 1. -3).
10. Suppose that T: R R is a linear transfomation with T(1.0,1) (1,2,0.1).
T(1,1.0)-(2.1,1,0), T(0,1,0)-(1-2,1.1). Find the standard matrix for T.
11. Assume u-(1.0,0,-1), v-(3,2.7,3), vy-(2,1.3.2), and v3-(5,2,9,5).
Show that u is in the orthogonal complement of W=span(v1.V2,V3).
12. Let W be the intersection of the planes 2r-y+z%3D0 and r-2y+2 0 in R3.
Find parametric equations for W-
[26 14]
13. Detemine the rank and nullity of the matrix C=0 1-1
[2 7 13
14. Let W be the subspace of R spanned by the vectors v=(1,0,7). -(6,1,7), and
V3-(14,-1,13). Find bases for W and W-
15. Find the standard matrix for the orthogonal projection of R onto the subspace
spanned by a=(1,1) and a-(0.1).
[10]
16. Find the least squares solution of Ax-b where =01
63=
11
17. Find the least squares straight line fit y ar+b t
the points (2,2). (4,3), and (6.7).
18. Use the Gram-Schmidt process to transform the given basis (W, W, W3} into an
orthogonal basis where wi (1,1,2), w (0,1.1), and w; - (-1,2,1).
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