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Practice questions - Linear Algebra/ Advanced Math Let...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21...
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21 Find X1 X2 and enter your answer in the box below. X1 X2 = Number We then apply Gram-Schmidt to find an orthonormal basis for W. V1 = X1 v2 = x2 - projv112 Find V2 and enter your answer in the box below. We then normalise the basis {V1, V2} to form an orthonormal basis {01, 12} (0) in Maple syntax, should be...
Problem #3: Let R4 have the inner product <u, v> = ulv1 + 2u2v2 + 3u3v3...
Problem #3: Let R4 have the inner product <u, v> = ulv1 + 2u2v2 + 3u3v3 + 40404 (a) Let w = (0,9,5,-2). Find llwll. (b) Let W be the subspace spanned by the vectors U1 = = (0,0, 2, 1), and u2 = (-3,0,–2, 1). Use the Gram-Schmidt process to transform the basis {uj, u2} into an orthonormal basis {V1, V2}. Enter the components of the vector v2 into the answer box below, separated with commas.
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find...
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
question 3 (b) Problem #3: Let R4 have the inner product <u, v>-#1v1 + 2112v2 +...
question 3 (b)
Problem #3: Let R4 have the inner product <u, v>-#1v1 + 2112v2 + 31/3V3 + 414V4 (a) Let w (0, 6, 3,-1). Find |w (b) Let Wbe the subspace spanned by the vectors u (0, 0, 2,1), and u2-,0,,-1) Use the Gram-Schmidt components of the vector v2 into the answer box below, separated with commas process to transform the basis fui. u2 into an orthonormal basis fvi, v23. Enter the Enter your answer symbolically as in these...
QUESTION 1 Let V-L2([0,1 ],C) and > : Vx-СУч . Г f(x)g(x)dx be an inner product...
QUESTION 1 Let V-L2([0,1 ],C) and > : Vx-СУч . Г f(x)g(x)dx be an inner product on V Let gor 91, 92, 93:0,1]R be given by gox)-1,g1(x)-x, 920x)-x2, g3(x) -x3 and consider the following subset S = { go, g 1, g 2, g3JC V. After applying the Gram-Schmidt process the following set of vectors T = {vo, vľ, V2, V3} is an orthonormal set, where V1, V2, V3, and V4 are given by: O vo= 1, v,-V3(2x-1), v,-V5 (6x2-6x...
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0...
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
I am not sure where to start on this linear algebra question. The set of vectors...
I am not sure where to start on this linear algebra
question.
The set of vectors for part a is these ones:
216 131 6. (a) [2] Is the set of vectors in Question 5 (b) a spanning set for R3? (b) [5] Let 01 U2 and vz Find (with justification) a vector w R4 such that w¢ Span何,v2, v3} (c) [3 In (b), is the set {oi,T2, T, a basis for R4? Justify your answer.
-247 -3 2. Let V1 = 1 , V , and V3 = , let B...
-247 -3 2. Let V1 = 1 , V , and V3 = , let B = (V1, V2, V3), and let W be the subspace spanned -2 by B. Note that B is an orthogonal set. 21 with respect to B, without inverting any matrices or a. [1 point] Find the coordinates of ū= 1: L 6 solving any systems of linear equations. 5 637 10 16. it point Find the sector in We st o b. [1 point]...
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29...
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21 Find X1 X2 and enter your answer in the box below. X1 X2 = Number We then apply Gram-Schmidt to find an orthonormal basis for W. V1 = X1 v2 = x2 - projv112 Find V2 and enter your answer in the box below. We then normalise the basis {V1, V2} to form an orthonormal basis {01, 12} (0) in Maple syntax, should be...
Problem #3: Let R4 have the inner product <u, v> = ulv1 + 2u2v2 + 3u3v3 + 40404 (a) Let w = (0,9,5,-2). Find llwll. (b) Let W be the subspace spanned by the vectors U1 = = (0,0, 2, 1), and u2 = (-3,0,–2, 1). Use the Gram-Schmidt process to transform the basis {uj, u2} into an orthonormal basis {V1, V2}. Enter the components of the vector v2 into the answer box below, separated with commas.
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
question 3 (b)
Problem #3: Let R4 have the inner product <u, v>-#1v1 + 2112v2 + 31/3V3 + 414V4 (a) Let w (0, 6, 3,-1). Find |w (b) Let Wbe the subspace spanned by the vectors u (0, 0, 2,1), and u2-,0,,-1) Use the Gram-Schmidt components of the vector v2 into the answer box below, separated with commas process to transform the basis fui. u2 into an orthonormal basis fvi, v23. Enter the Enter your answer symbolically as in these...
QUESTION 1 Let V-L2([0,1 ],C) and > : Vx-СУч . Г f(x)g(x)dx be an inner product on V Let gor 91, 92, 93:0,1]R be given by gox)-1,g1(x)-x, 920x)-x2, g3(x) -x3 and consider the following subset S = { go, g 1, g 2, g3JC V. After applying the Gram-Schmidt process the following set of vectors T = {vo, vľ, V2, V3} is an orthonormal set, where V1, V2, V3, and V4 are given by: O vo= 1, v,-V3(2x-1), v,-V5 (6x2-6x...
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
I am not sure where to start on this linear algebra
question.
The set of vectors for part a is these ones:
216 131 6. (a) [2] Is the set of vectors in Question 5 (b) a spanning set for R3? (b) [5] Let 01 U2 and vz Find (with justification) a vector w R4 such that w¢ Span何,v2, v3} (c) [3 In (b), is the set {oi,T2, T, a basis for R4? Justify your answer.
-247 -3 2. Let V1 = 1 , V , and V3 = , let B = (V1, V2, V3), and let W be the subspace spanned -2 by B. Note that B is an orthogonal set. 21 with respect to B, without inverting any matrices or a. [1 point] Find the coordinates of ū= 1: L 6 solving any systems of linear equations. 5 637 10 16. it point Find the sector in We st o b. [1 point]...
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
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