2.28 Find a set to span the given subspace of the given space. (Hint. Parametrizeeach.)(a) the xz-plane in RX.(b) { | y ] | 3x + 2y + z = 0} in R³

We have to find a set to span the given subspace of the given space.

Answered: 2.28 Find a set to span the given…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

See similar textbooks

Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
Let V = { [x y z] in ℝ^3 ∶ z = 2x - y }. Is V a subspace of ℝ^3? If it is, what is the dimension of V? Any help (especially with details) would be greatly appreciated.
Is the set M={1/n | n ε z+} compact as a subspace of R?
(a) find the orthogonal complement S⊥, and (b) find the direct sum S⊕S⊥. S is the subspace of R3 consisting of the xz-plane.
Which of the listed sets is a vector subspace of the space V=R^2 over the field R?
Let W1 and W2 be subspaces of a vector space V having ilimensions mand n, respectively, where m >= n .(a ) Prove that dim(W1 ∩ W2)<= n .(b ) Prove that dim(W1 + W2) <= m + n.
W is a subspace of R4 consisting of vectors of the form. Determine dim(W) when the components of x satisfy the given conditions.
Suppose U1; U2; :::; Um are Önite-dimensional subspaces of V .Prove thatU1 + U2 + ::: + Um is Önite-dimensionalanddim(U1 + U2 + ::: + Um) dim U1 + dim U2 + ::: + dim Um
Find the orthogonal projection of the vector [ 49 49 49] onto the subspaces of R3 spanned by [2 3 6], and [3 -6 2].
Let C[−π, π] be the vector space of functions that are continuous over the interval [−π, π]. Find the dimensionof the subspace of C[−π, π] that is spanned by the set {1, cos(2x), cos^2(x)}.
Consider the subspace W of D, given by W = span(e2x, e2x cos x, e2x sin x). (a) Find the matrix of D with respect to B = {e2x, e2x cos x, e2x sin x}. (b) Compute the derivative of f(x) = 3e2x - e2xcosx+ 2e2x sin x indirectly, using and verify that it agrees with f' (x) as computed directly.

SEE MORE QUESTIONS

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

2.28 Find a set to span the given subspace of the given space. (Hint. Parametrize each.) (a) the xz-plane in R3