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.
a) Find a subset of the given vectors that forms a basis for the space spanned by these vectors.
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.
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...
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.
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
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, ).
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Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
2. Consider the vectors -11 -11] 31, ; [-9] 13 -2. V2 = V = 14 -51 3 V3 = 3 [-14] -12 16 16 V4 = ' Vs = (a) Find a subset of {v1, V2, V3, V4, Vs} that is linearly independent and contains as many vectors as possible. (b) Prove that your answer to (a) indeed gives a maximal independent subset by showing that your subset has the same span as the original set of vectors {V1,...
8. (a) Use the Gram-Schmidt procedure to produce an orthonormal basis for the sub space spanned by W = Do not change the order of the vectors. (b) Express the vector x = as a linear combination of the orthonormal basis obtained in part (a).
please give the correct answer with explanations, thank you
Let S {V1, V2, V3, V4, Vs} be a set of five vectors in R] Let W-span) When these vectors are placed as columns into a matrix A as A-(V2 V3 r. ws). and Asrow-reduced to echelon form U. we have U - -1 1 013 001 1 state the dimension of W Number 2. State a boss B for W using the standard algorithm, using vectors with a small as...
Show that w is in the subspace of R4 spanned by vy. Vz, and v3, where these vectors are defined as follows 2 -4 w= 5 V21 - 2 -4 17 To show that w is in the subspace, express was a linear combination of v. Vz, and V3 The vector w is in the subspace spanned by V, V2, and Vy. It is given by the formula w= (O) v * (IDv. O (Simplify your answers. Type integers or...