5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1...
Let --0) --- () -- () = 0 V = 2 . V = 5 , V3 = 8 . V = 11 (a) Find the reduced row echelon form R = (v1, V, V, val of A = (v1, V2, V3, V4]. (b) Write vs and va as linear combinations of vand va (c) Write V3 and Va as linear combinations of vi and V2. (d) Find a basis for the row space of A. (e) Find a basis...
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...
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...
Please show work
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...
Consider the following three vectors in
; v1 = (1, 7, −2), v2 = (4, 3, 5), v3 = (2, −11, 9):
i) Say whether v1, v2, v3 are linearly dependent or linearly
independent. (Justify)
ii) Say if v1, v2, v3 generate
. (justify)
iii) If it exists, determine the constants c1, c2, c3, such that
c1v1 + c2v2 + c3v3 = (0, −5, 13/5), or argue why it cannot be
written as a linear combination.
We were unable to...
008 10.0 points The set of vectors {v1, v2, v3) is a spanning set for R'‘ when Determine c2 so that for an arbitrary x in R3 1. c2 =-2x3+ 5x2 + 4x1 2. c2 = 2x3-5x2 + 4x1 3. c2 = 2x3+ 5x2-4x1 5. c2 =-2x3-5x2 + 4x1 6. c2 223-5x2-4x1
Can I get help with questions 2,3,4,6?
be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2, 1), V2 = (2,4, 2), V3 = (0,1,0), and v4 = (3, 7,3). (a) (2 points) Obtain a basis for R3 that includes as many of these vectors as possible. (b) (4 points) Obtain the orthogonal projection matrices onto the plane V = span{v1, v3} and its perpendicular complement V+. (c) (2 points) Use this result to decompose the vector b= (-1,1,1) into a...
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.