Homework Answers
3t Let W be the set of all vectors of the form 5 +5 5s Show...
3t Let W be the set of all vectors of the form 5 +5 5s Show that W is a subspace of R* by finding vectors u and v such that W=Span{u,v). 5s Write the vectors in Was column vectors 31 5 4 5t = su + tv 5s 5s What does this imply about W? O A. W = Span(u,v} OB. W = Span{s.t O C. Ws+t OD. W=u+v
Let w be a subspace of R", and let wt be the set of all vectors...
Let w be a subspace of R", and let wt be the set of all vectors orthogonal to W. Show that wt is a subspace of R" using the following steps. a. Take z in wt, and let u represent any element of W. Then zu u = 0. Take any scalar c and show that cz is orthogonal to u. (Since u was an arbitrary element of W, this will show that cz is in wt.) b. Take z,...
2r - 38 + 4t ret Let W be the set of vectors in R4 of...
2r - 38 + 4t ret Let W be the set of vectors in R4 of the form Is W a subspace of R4? Why or why not? - 8 3s + 3t
11.Span: Problem 12 Previous Problem Problem List Next Problem [ –2s – 1 (1 point) Let...
11.Span: Problem 12 Previous Problem Problem List Next Problem [ –2s – 1 (1 point) Let W be the set of all vectors of the form 3s – 3t . Find vectors ū and V in Rº such that W = span {ū, v}. | 3t – 4s]
(10) Let ū ER. Show that M = {ū= | ER*:ūū= 0) is a subspace of...
(10) Let ū ER. Show that M = {ū= | ER*:ūū= 0) is a subspace of R'. Definition: (Modified from our book from page 204.) Let V be a subspace of R". Then the set of vectors (61, 72, ..., 5x} is a basis for V if the following two conditions hold. (a) span{61, 62,...,x} = V (b) {61, 62, ..., 5x} is linearly independent. Definition: Standard Basis for R" The the set of vectors {ēi, 72, ..., en) is...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1),...
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
Question 5 Let V be a subspace of R100, and let S be a set of...
Question 5 Let V be a subspace of R100, and let S be a set of vectors such that y = = span(S). (S is a spanning set for V.) Build a matrix A using the vectors of S as columns. The dimension of V must be equivalent to all of the following EXCEPT: the number of nonzero rows in a REF of A the number of vectors in S the rank of A O the number of "leading 1s"...
Linear Algebra Advanced Let A be vectors in R". Show that the set of all vectors...
Linear Algebra Advanced
Let A be vectors in R". Show that the set of all vectors B in R" such that B is perpendicular to A is a subspace of R". In other words shovw W Be R"IA B-0 for a vector Ae R" is a subspace.
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...
3t Let W be the set of all vectors of the form 5 +5 5s Show that W is a subspace of R* by finding vectors u and v such that W=Span{u,v). 5s Write the vectors in Was column vectors 31 5 4 5t = su + tv 5s 5s What does this imply about W? O A. W = Span(u,v} OB. W = Span{s.t O C. Ws+t OD. W=u+v
Let w be a subspace of R", and let wt be the set of all vectors orthogonal to W. Show that wt is a subspace of R" using the following steps. a. Take z in wt, and let u represent any element of W. Then zu u = 0. Take any scalar c and show that cz is orthogonal to u. (Since u was an arbitrary element of W, this will show that cz is in wt.) b. Take z,...
2r - 38 + 4t ret Let W be the set of vectors in R4 of the form Is W a subspace of R4? Why or why not? - 8 3s + 3t
11.Span: Problem 12 Previous Problem Problem List Next Problem [ –2s – 1 (1 point) Let W be the set of all vectors of the form 3s – 3t . Find vectors ū and V in Rº such that W = span {ū, v}. | 3t – 4s]
(10) Let ū ER. Show that M = {ū= | ER*:ūū= 0) is a subspace of R'. Definition: (Modified from our book from page 204.) Let V be a subspace of R". Then the set of vectors (61, 72, ..., 5x} is a basis for V if the following two conditions hold. (a) span{61, 62,...,x} = V (b) {61, 62, ..., 5x} is linearly independent. Definition: Standard Basis for R" The the set of vectors {ēi, 72, ..., en) is...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
Question 5 Let V be a subspace of R100, and let S be a set of vectors such that y = = span(S). (S is a spanning set for V.) Build a matrix A using the vectors of S as columns. The dimension of V must be equivalent to all of the following EXCEPT: the number of nonzero rows in a REF of A the number of vectors in S the rank of A O the number of "leading 1s"...
Linear Algebra Advanced
Let A be vectors in R". Show that the set of all vectors B in R" such that B is perpendicular to A is a subspace of R". In other words shovw W Be R"IA B-0 for a vector Ae R" is a subspace.
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...
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