Linear Algebra AdvancedHomework Answers
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Linear Algebra Advanced
Let A be vectors in R". Show that the set of all vectors...
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,...
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector...
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...
Help on this question of Linear Algebra, thanks. Let W be a nonzero subspace of R"....
Help on this question of Linear Algebra, thanks.
Let W be a nonzero subspace of R". Prove that any two bases for W contain the same number of vectors.
(6) In R3, let W be the set of solutions of the homogeneous linear equation r...
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W
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.
6. Let W be the set of all vectors of the form W {(a,b,c): a –...
6. Let W be the set of all vectors of the form W {(a,b,c): a – 2b + 4z = 0} Is W a subspace of the vector space V = R3?
Problem 1: consider the set of vectors in R^3 of the form: Material on basis and...
Problem 1: consider the set of vectors in R^3 of the
form:
Material on basis and dimension Problem 1: Consider the set of vectors in R' of the form < a-2b,b-a,5b> Prove that this set is a subspace of R' by showing closure under addition and scalar multiplication Find a basis for the subspace. Is the vector w-8,5,15> in the subspace? If so, express w as a linear combination of the basis vectors for the subspace. Give the dimension of...
Linear Algebra Question: Forgot to include the vaules of u, v and w.
Linear Algebra Question:
Forgot to include the vaules of u, v and w.
:]suchthata,b,c,dso 6. 18 Points] Show that V, the set of all 2x2 matrices of the form such that a, b, c, d s0, is not a subspace. s. I5 Points each] Let ü = (2,-6, 2), v = (0, 4,-2), and w-(2, 2,-4) a. Find a vector that is orthogonal to both v and w using the cross product. b. Find the area of the parallelogram in...
linear algebra- Linear independence Problems 1. Show that the following sets of vectors in R" are...
linear algebra- Linear independence
Problems 1. Show that the following sets of vectors in R" are linearly dependent: U = (-1,2,4) and V = (5.-10,--20) in R. (b) U = (3,-1), V =(4,5) and W = (-4,7) in R2. 2. Are the following sets of vectors in R3 linearly independent or linearly dependent? Show work. (-3,0,4), (5,-1, 2) and (1, 1,3) (b) (-2,0,1), (3, 2,5), (6,-1,1) and (7,0,-2)
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 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,...
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...
Help on this question of Linear Algebra, thanks.
Let W be a nonzero subspace of R". Prove that any two bases for W contain the same number of vectors.
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W
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.
6. Let W be the set of all vectors of the form W {(a,b,c): a – 2b + 4z = 0} Is W a subspace of the vector space V = R3?
Problem 1: consider the set of vectors in R^3 of the
form:
Material on basis and dimension Problem 1: Consider the set of vectors in R' of the form < a-2b,b-a,5b> Prove that this set is a subspace of R' by showing closure under addition and scalar multiplication Find a basis for the subspace. Is the vector w-8,5,15> in the subspace? If so, express w as a linear combination of the basis vectors for the subspace. Give the dimension of...
Linear Algebra Question:
Forgot to include the vaules of u, v and w.
:]suchthata,b,c,dso 6. 18 Points] Show that V, the set of all 2x2 matrices of the form such that a, b, c, d s0, is not a subspace. s. I5 Points each] Let ü = (2,-6, 2), v = (0, 4,-2), and w-(2, 2,-4) a. Find a vector that is orthogonal to both v and w using the cross product. b. Find the area of the parallelogram in...
linear algebra- Linear independence
Problems 1. Show that the following sets of vectors in R" are linearly dependent: U = (-1,2,4) and V = (5.-10,--20) in R. (b) U = (3,-1), V =(4,5) and W = (-4,7) in R2. 2. Are the following sets of vectors in R3 linearly independent or linearly dependent? Show work. (-3,0,4), (5,-1, 2) and (1, 1,3) (b) (-2,0,1), (3, 2,5), (6,-1,1) and (7,0,-2)
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
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