Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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).
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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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