Find an orthonormal basis for the given subspace. (Enter sqrt(n) for n.) S = span
(a) Find an orthonormal basis for the subspace U = span ((1, −1, 0, 1, 1),(3, −3, 2, 5, 5),(5, 1, 3, 2, 8)) of R 5 . (b) Express the vectors (0, −6, −1, 5, −1) as linear combinations of the orthonormal basis obtained in part (a). (c) Which of the standard basis vectors lie in U?
4. Use the Gram-Schmidt Process to find an orthonormal basis for the subspace of R5 defined by 2 S-span 0 2
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Find an orthonormal basis QWL of WL and find the dimension of WL 3. GIven a vector u- . find the Qw coordinate of Projw(v) . find the Qwa coordinate of Projwi (v) » find the coordinate...
Find an orthonormal basis for the subspace of R3 spanned by Extend the basis you found to an orthonormal basis for R 3 (by adding a new vector or vectors). Is there a unique way to extend the basis you found to an orthonormal basis of R3 ? Explain.
Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and A xyT + (i) Show that x+y and x -y are eigenvectors of A. What are their corresponding eigenvalues? (ii) Show that 0 is an eigenvalue of R" with n - 2 linearly independent eigenvectors. (iii) Explain why A is diagonalizable. Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and A xyT + (i) Show that x+y...
(1 point) Find a basis of the given subspace by deleting linearly dependent vectors. span of 0, 0 LoJ LO 0 0 A basis is
Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and T A= xx SL (i) Show that N(A (ii) Show that the rank of A is 2 (iii Show that x and y are eigenvectors of A for an eigenvalue X of A. What is A? Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and T A= xx SL (i) Show that N(A (ii) Show that the...
(a) Find an orthonormal basis for the linear subspace V of R4 generated by the vectors 1 1 1 1 2 (b) What is the projection of the vector on the linear subspace V?
3. Use the Gram-Schmidt method to find an orthonormal basis of the vector space Span < 2
T1 4r . Find a orthonormal basis for the following subspace of R*: x2: T2 2 T2