a) Is the set W = {(x, y, 1) | x, y are real numbers} a subspace of R^3 ? (b) Is the set W = {(x, y, z) | x + y + z = 0 and x, y, and z are real numbers} a subspace of R^3 ?
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(a) Is the set W = {(x, y, 1) | x, y are real numbers} a subspace of R^3 ?
(b) Is the set W = {(x, y, z) | x + y + z = 0 and x, y, and z are real numbers} a subspace of R^3 ?
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- 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.Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.How would I find whether there is a linear algebra subspace in R^3, inclusion of zero vector, closure under vector addition or scalar multiplication?
- The span of a set of vectors from a vector space V is a subspace of V. true or false?Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1)(2) On the plane determined by (1, 2, 1) and (1, −1, 1)(3) On the subspace spanned by (1, 2, 1), (1, −1, 1) and (3, 0, −3)Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.
- what is the dimension of the subspace H knowing that it is not independentWe denote the subspace spanned by the first two columns of A by U, and the subspace spanned by the last three columns of A by V . It's asked to determine a basis of U ∩ V, Please do it step by step, I got to the point of determining the null space which is (1/3, -1/3, 1, 1, 1)x5, but what happens after that?plz do not us these topics like rank, vector spaces, subspaces, column spaces, or their associated theory to prove
- plz do not use the topics rank, vector spaces, subspaces, column spaces, etc. or their associated theory to prove the answerHow to find the subspace of R4 ? I have attached the image with this question Its kinda very complicated to undertand it properly.Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by −(4x2+5x+4), 1−(6x2+17x) and −(x2+2). The dimension of the subspace H is . Is {−(4x2+5x+4),1−(6x2+17x),−(x2+2)} a basis for P2? choose Be sure you can explain and justify your answer. A basis for the subspace H is { }. Enter a polynomial or a comma separated list of polynomials