3. (12 pts) Find a subset of vectors that forms a basis for the space spated...
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.
3. (12 pts) Find a subset of vectors that forms a basis for the space spanned by Vi = (1, -2,0,3), 02 = (2,-5, -3,6), V3 = (0,1,3,0), 04 = (-2, 1, -4,7), v5 = = (-5, 8,-1, -2). Then express the other vector(s) as a linear combination of the basis vectors.
a) Find a subset of the given vectors that forms a basis for the space spanned by these vectors. b) Express each vector not in the basis as a linear combination of the basis vectors.c) Use the vectors V1, V2, V3, V4, Vs to construct a basis for R4.
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
Linear Algebra 6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2 = (-2,3,1,0), V3 =(4,-5, 9,4), V4 = (0,4,2, -3) V5 = (-7, 18, 2, -8) that forms a basis for the space spanned by these vectors. (b) Use (a) to express each vector not in the basis as a linear combination of the basis vectors. (c) Let Vi V2 A= V3 V4 Use (a) to find the dimension of row(A), col(A), null(A), and of...
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...
4.) Consider a system in 3-dimensions with basis vectors {v1, v2, vs}, where V 1 0 1 1 0 0 1 U3= 1 -1 0 The operator A when acted upon the basis vector ui gives a new vector X, with AvXy Σ ν X-Σ4υ Please write out the explicit expression for the 3 x 3 matrix A,, which is the operator in the v basis, in terms of ay and numbers (you can't just write v) (10-pts) Now lets...
4. (12 pts) Show the matrix operator T: RR given by the following equations is one-to-one; Find the standard matrix for the inverse operator T-l, and find T-(W1, 2, 3). w = x - 2:02 +2:23 w2 = 2.rı -23 W3 = 2.11 - 12 +23
3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis for the nullspace of (b) 4 points] Using the columns of A, find a basis for the column space of A (c) [2 points What are the dimensions of these spaces? (d) [2 points] ls the vector u-I1-1 0 ојт in the nullspace of A? Why? (e) [4 points] Is the vector w-17-9 9-9]T İn the column space of A? If so, express w...
Problem 4 A set of vectors is given by S = {V1, V2, V3} in R3 where eV1 = 1 5 -4 7 eV2 = 3 . eV3 = 11 -6 10 a) [3 pts) Show that S is a basis for R3. b) (4 pts] Using the above coordinate vectors, find the base transition matrix eTs from the basis S to the standard basis e. Then compute the base transition matrix sTe from the standard basis e to the...