


6 Determine a basis for the wll space of A and We dinnsion (b) (4 pts.)...
Question 4 2 pts Determine whether the vector u is in the column space of the matrix A and whether it is the null space of A. 1 0 3 1 -2 1 - 4 U = 3 3 0 4 - 1 3 6 Not in Col A in Nul A In Col A, not in Nul A Not in ColA, not in Nul A In Col A and in Nul A Question 5 1 pts 1 co 2...
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of Re"). 2. (12 pts) Given the matrix in a R R-E form: -21 1 [1 0 0 0 3 0 1 1 0 - 2 0 0 0 1 0...
6. Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): 3 -1 2 3 1 5 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, 9(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2 x 2 matrices: (You'd decided what the inner product was on...
Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): -1 1 ( 2 5 3 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, g(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2x2 matrices: (You'd decided what the inner product was on a previous math...
4. (11 pts) Find a subsct of vectors that forms a basis for the space spanned by -(1,2,0,3), ty=(8, 1,6,9), = (0, -1,3,0), t = (2-1,2,1), us = (5.-1,7,5). Then express the other vector(s) is a linear combination of the basis vectors
Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of A d) For each column vector which is not a basis vector that you obtained in c), express it as a linear combination of the basis vectors for the range of...
3. (12 pts) Find a subset of vectors that forms a basis for the space spanned by v1 = (1, 2, 2, -1), v2 = (-3, -6, -6,3), v3 = (4,9, 9, -4), v4 = (-2,-1,-1,2), v5 = (5,8,9,-5) Then express the other vector(s) as a linear combination of the basis vectors.
no calculator please
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a + 3b) (which is a subspace of R®). 2. (12 pts) Given the matrix in a R R-E form: 1000 3 0110-2 00011 0 0 0 0 0 (a) (6 pts) Find rank(A)...
3. (12 pts) Find a subset of vectors that forms a basis for the space spated by 11 = (1.22. - 1), 1 = (-3, -6, -6,3). Es =(4,9,9,-4), 4 = (-2,-1,-1,2), 3 =(5,8,9,-5). Then express the other vector(s) as a linear combination of the basis vectors 4. 12 pts) Show the matrix operator T: - R given by the following equations is one-to-one Find the standard matrix for the inverse operator T-!, and find T-2, 43, ).
1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a +36) (which is a subspace of R).