![7. (10pts) Show that {u1, U2, u3}is an orthogonal basis for R°. Then express x as a linear combination of the us. -i]--}-|--](http://img.homeworklib.com/questions/66a6a190-b50e-11eb-9e1a-f1e98c31ac46.png?x-oss-process=image/resize,w_560)
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7. (10pts) Show that {u1, U2, u3}is an orthogonal basis for R°. Then express x as...
1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for...
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1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Show that (u, u2 ub) is an orthogonal basis for R Thon express as a inear...
Show that (u, u2 ub) is an orthogonal basis for R Thon express as a inear of the u's Which of the following cniteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of IR? Select all that apply A. The vectors must span W B. The vectors must all have a length of 1 D C. The distance between any pair of distinct vectors must be constant D. The vectors must form...
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul , u2 , u3 and 14 are orthogonal. u1+ 7 U2 ll4 (1 point) 0 Given...
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul , u2 , u3 and 14 are orthogonal. u1+ 7 U2 ll4
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul...
(1 point) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement....
(1 point) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement. O A. We only know that span{u1, U2, U3, u4} span{u1, u2, u3} . B. There is no obvious relationship between span{u1, U2, uz} and span{u1, U2, U3, u4} . C. span{u1, U2, U3} = span{u1, U2, U3, u4} when none of {u1, U2, uz} is a linear combination of the others. D. We only know that span{u1, U2, U3} C span{u1, U2, U3,...
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...
(1 point) Let u4 be a linear combination of {u1, U2, u3}. Select the best statement....
(1 point) Let u4 be a linear combination of {u1, U2, u3}. Select the best statement. OA. {u1, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. OB. {ui, U2, U3, U4} is always a linearly dependent set of vectors. OC. {ui, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, U2, U3, U4} is a linearly...
linear algebra -Answer the following question: If S ={ ui, U2, U3} is a set of...
linear algebra
-Answer the following question: If S ={ ui, U2, U3} is a set of vectors in the vector space R', where új =(2,0,1), uz =(0,1,0), and uz =(-2,0,0). i) Determine whether the vector v=(2,4,2) is a linear combination of uı, U2 and uz or not. ii) Show that the set S is a spanning set for R or not. Why? iii) Is the set S linearly independent in R? iv) Determine whether S is basis for R' or...
Show that ((U1, U2, U3), (V1, V2, V3)) = U1v1 – U202 – U3V3 is not...
Show that ((U1, U2, U3), (V1, V2, V3)) = U1v1 – U202 – U3V3 is not an inner product on R3.
(1 point) Assume ug is not a linear combination of {u1, 42, u3}. Select the best...
(1 point) Assume ug is not a linear combination of {u1, 42, u3}. Select the best statement. A. {u1, U2, U3, U4} is never a linearly independent set of vectors. B. {U1, U2, U3, U4} is always a linearly independent set of vectors. C. {ui, U2, U3, U4} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, 42, uz, u4} could be a linearly independent or linearly dependent set of vectors...
Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r...
Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r], the set of all degree 2 or less polynomial functions. (c) Show that if A is invertible, then det A (Note: Show it for any det A-1 square matrix, showing it for a 2 x 2 matrix...
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1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Show that (u, u2 ub) is an orthogonal basis for R Thon express as a inear of the u's Which of the following cniteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of IR? Select all that apply A. The vectors must span W B. The vectors must all have a length of 1 D C. The distance between any pair of distinct vectors must be constant D. The vectors must form...
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul , u2 , u3 and 14 are orthogonal. u1+ 7 U2 ll4
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul...
(1 point) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement. O A. We only know that span{u1, U2, U3, u4} span{u1, u2, u3} . B. There is no obvious relationship between span{u1, U2, uz} and span{u1, U2, U3, u4} . C. span{u1, U2, U3} = span{u1, U2, U3, u4} when none of {u1, U2, uz} is a linear combination of the others. D. We only know that span{u1, U2, U3} C span{u1, U2, U3,...
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...
(1 point) Let u4 be a linear combination of {u1, U2, u3}. Select the best statement. OA. {u1, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. OB. {ui, U2, U3, U4} is always a linearly dependent set of vectors. OC. {ui, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, U2, U3, U4} is a linearly...
linear algebra
-Answer the following question: If S ={ ui, U2, U3} is a set of vectors in the vector space R', where új =(2,0,1), uz =(0,1,0), and uz =(-2,0,0). i) Determine whether the vector v=(2,4,2) is a linear combination of uı, U2 and uz or not. ii) Show that the set S is a spanning set for R or not. Why? iii) Is the set S linearly independent in R? iv) Determine whether S is basis for R' or...
Show that ((U1, U2, U3), (V1, V2, V3)) = U1v1 – U202 – U3V3 is not an inner product on R3.
(1 point) Assume ug is not a linear combination of {u1, 42, u3}. Select the best statement. A. {u1, U2, U3, U4} is never a linearly independent set of vectors. B. {U1, U2, U3, U4} is always a linearly independent set of vectors. C. {ui, U2, U3, U4} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, 42, uz, u4} could be a linearly independent or linearly dependent set of vectors...
Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r], the set of all degree 2 or less polynomial functions. (c) Show that if A is invertible, then det A (Note: Show it for any det A-1 square matrix, showing it for a 2 x 2 matrix...
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