![Question 2. (15 pts) Let vi=(-3 0 6), v2= (-2 2 3], V3= (0 - 6 37, and w= [1 11 9. (1). Determine if w is in the subspace](http://img.homeworklib.com/questions/84924ab0-fdb7-11ea-a209-01567706fe2e.png?x-oss-process=image/resize,w_560)
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![2 2 Vi = 13] U2= 2 V3 = -6 3 3 Let wi Civ, +C₂ V2 + (₂ V3. o • 6:40 - 3 In augmented form, we have. 3 o 2 14 6 3 3 9 Applying](http://img.homeworklib.com/questions/dd42b250-1018-11eb-8861-f7008fecd6f0.png?x-oss-process=image/resize,w_560)
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1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the...
Question 2. (15 pts) Let Vi= (-3 0 6)", v2= (-2 2 3)", V3= [0 -...
Question 2. (15 pts) Let Vi= (-3 0 6)", v2= (-2 2 3)", V3= [0 - 6 3)", and w= [1 14 9)? (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors Vi, V2, V3 linearly dependent or independent? Justify your answer.
Question 2. (15 pts) Let vi= (-3 0 6)", V2= (-2 2 317, V3= [0 -...
Question 2. (15 pts) Let vi= (-3 0 6)", V2= (-2 2 317, V3= [0 - 6 3)", and w=(1 14 9) (1). Determine if w is in the subspace spanned by va, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer.
Let v1= [−3 0 6]T , v2= [−2 2 3]T , v3= [0 − 6 3]T...
Let v1= [−3 0 6]T , v2= [−2 2 3]T , v3= [0 − 6 3]T , and w= [1 14 9]T . (1). Determine if w is in the subspace spanned by v1, v2, v3. (2). Are the vectors v1, v2, v3 linearly dependent or independent? Justify your answer.
Question 2. (15 pts) Let vi= [-3 0 6)". Vy=[-2 2 3". Vg= [0 - 6...
Question 2. (15 pts) Let vi= [-3 0 6)". Vy=[-2 2 3". Vg= [0 - 6 3), and w=[1 14 97 (1). Determine if w is in the subspace spanned by V. V2 V3. (2). Are the vectors Vi, V2, V3 linearly dependent or independent? Justify your answer.
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...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
1. Find A if (2A)' = [ : :] 2. Determine if {(x,y) : x -...
1. Find A if (2A)' = [ : :] 2. Determine if {(x,y) : x - y = 1) is a subspace of vector space V - R 3. Let vi, V2, V3 be three linearly independent vectors in a vector space V. Is the set {v1 - 2v2, 2v2 - 3v3, 3V3 - Vi} linearly independent or linearly dependent? Prove your answer.
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
Consider the following three vectors in ; v1 = (1, 7, −2), v2 = (4, 3,...
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...
Question 2. (15 pts) Let Vi= (-3 0 6)", v2= (-2 2 3)", V3= [0 - 6 3)", and w= [1 14 9)? (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors Vi, V2, V3 linearly dependent or independent? Justify your answer.
Question 2. (15 pts) Let vi= (-3 0 6)", V2= (-2 2 317, V3= [0 - 6 3)", and w=(1 14 9) (1). Determine if w is in the subspace spanned by va, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer.
Question 2. (15 pts) Let vi= [-3 0 6)". Vy=[-2 2 3". Vg= [0 - 6 3), and w=[1 14 97 (1). Determine if w is in the subspace spanned by V. V2 V3. (2). Are the vectors Vi, V2, V3 linearly dependent or independent? Justify your answer.
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...
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
1. Find A if (2A)' = [ : :] 2. Determine if {(x,y) : x - y = 1) is a subspace of vector space V - R 3. Let vi, V2, V3 be three linearly independent vectors in a vector space V. Is the set {v1 - 2v2, 2v2 - 3v3, 3V3 - Vi} linearly independent or linearly dependent? Prove your answer.
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
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...
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