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![The given vectors in Rare V = wenn (6) A=[û z ♡ Ą E] -2 ora-d - is Nī کم و با م م به 6 4 2 - 2 2 3 R, R3 4 -- ì - 00 آله وسلم](http://img.homeworklib.com/questions/2aceb790-e442-11ea-a662-8dcadb63a13e.png?x-oss-process=image/resize,w_560)
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
Can I get help with questions 2,3,4,6? be the (2) Determine if the following sequences of vectors vi, V2, V3 are linear...
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...
2. Consider the vectors -11 -11] 31, ; [-9] 13 -2. V2 = V = 14...
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,...
please answer the following question with detailed step 1 1. Consider vi = 2 V2 =...
please answer the following question with detailed step
1 1. Consider vi = 2 V2 = a and v3 = -1 (a) Find the value(s) of a such that 01,02 and v3 are linearly dependent and write Vi as a linear combination of v2 and 03, if possible. (b) Suppose a = 0, write v = 2 as a linear combination of v1, V2 and 03. (c) Suppose a = 0, use the Gram-Schmidt process to transform {V1, V2, V3}...
Linear Algebra 6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2...
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 show work Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 =...
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...
Let --0) --- () -- () = 0 V = 2 . V = 5 ,...
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...
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2,...
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...
sorry for the bad picture, and thanks for your assitance in advance :) Chapter 4, Section...
sorry for the bad picture, and thanks for your assitance in
advance :)
Chapter 4, Section 4.5, Question 17 Find a basis for the subspace of that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 0, 1), V3 = (4, 0, 1), V4 = (0, 0, -2) O vi and v3 form a basis for span {V1, V2, V3, V4}. O v3 and V4 form a basis for span {V1, V2, V3, V4}. O vi...
Problem 1. Let V1,...,V5 be vectors in R3, as shown in the four figures below. In...
Problem 1. Let V1,...,V5 be vectors in R3, as shown in the four figures below. In each figure, find all linearly dependent sets consisting of three of these five vectors, or else state that there are none if this is the case. No justification needed. (Note that in each of these figures, Vi and V2 span the displayed plane, V3 points "up" and is perpendicular to this plane, and for any other vector not in the plane, we draw a...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
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...
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,...
please answer the following question with detailed step
1 1. Consider vi = 2 V2 = a and v3 = -1 (a) Find the value(s) of a such that 01,02 and v3 are linearly dependent and write Vi as a linear combination of v2 and 03, if possible. (b) Suppose a = 0, write v = 2 as a linear combination of v1, V2 and 03. (c) Suppose a = 0, use the Gram-Schmidt process to transform {V1, V2, V3}...
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 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...
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...
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...
sorry for the bad picture, and thanks for your assitance in
advance :)
Chapter 4, Section 4.5, Question 17 Find a basis for the subspace of that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 0, 1), V3 = (4, 0, 1), V4 = (0, 0, -2) O vi and v3 form a basis for span {V1, V2, V3, V4}. O v3 and V4 form a basis for span {V1, V2, V3, V4}. O vi...
Problem 1. Let V1,...,V5 be vectors in R3, as shown in the four figures below. In each figure, find all linearly dependent sets consisting of three of these five vectors, or else state that there are none if this is the case. No justification needed. (Note that in each of these figures, Vi and V2 span the displayed plane, V3 points "up" and is perpendicular to this plane, and for any other vector not in the plane, we draw a...
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