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Homework Answers
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5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1...
5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1 = (1,1,1), V2 = (1,0,1), V3 = (3,2,1) coincides with R. (b) Determine if b= is in the column space of A = 13 1 11 2 0 1 . If yes, write bas a linear 1 1 1] combination of columns of A.
(1 point) 5 10 10 Let A = 2 7 10 and b= -5 -8 -11...
(1 point) 5 10 10 Let A = 2 7 10 and b= -5 -8 -11 Denote the columns of A by aj, a2, az , and let W = span {aj, 22,03}. Select Answer 1. Determine if b is in W Select Answer A 2. Determine if b is in {aj, az, az } How many vectors are in {aj, a2, az }? (For infinitely many, enter -1) How many vectors are in W? (For infinitely many, enter -...
1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by...
1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by a, a, ay, and let W = Span{a,,a,,a3} -26 2 3 a. Is b in {a,,a,,az)? How many vectors are in {a,az.az)? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {a,,a,,az)? Ο Νο Yes How many vectors are in {a,,a,a}? O A. Two OB. Infinitely...
Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote...
Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote the columns of A by a, a, az, and let W = Span{a.a.az). a. Is b in aa.az)? How many vectors are in a .a .a? b. Is bin W? How many vectors are in W? c. Show that a is in W. (Hint: Row operations are unnecessary.] a. Is b in {a .az.az)? No Yes O How many vectors are in aaa? A....
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ...,...
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
-247 -3 2. Let V1 = 1 , V , and V3 = , let B...
-247 -3 2. Let V1 = 1 , V , and V3 = , let B = (V1, V2, V3), and let W be the subspace spanned -2 by B. Note that B is an orthogonal set. 21 with respect to B, without inverting any matrices or a. [1 point] Find the coordinates of ū= 1: L 6 solving any systems of linear equations. 5 637 10 16. it point Find the sector in We st o b. [1 point]...
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...
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...
-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 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns...
1 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns of A by ay, az, az, and let W= = Span{a,,a,,az}. -34 2 -5 1 a. Is b in {a4, az, az}? How many vectors are in {aq,a2, az}? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {aq, az, az}? No Yes How many vectors...
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13...
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2 Q2l+3 Qsl). Then T-5sin (100Q) satisfies: -(A) 0ST<1.
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2...
5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1 = (1,1,1), V2 = (1,0,1), V3 = (3,2,1) coincides with R. (b) Determine if b= is in the column space of A = 13 1 11 2 0 1 . If yes, write bas a linear 1 1 1] combination of columns of A.
(1 point) 5 10 10 Let A = 2 7 10 and b= -5 -8 -11 Denote the columns of A by aj, a2, az , and let W = span {aj, 22,03}. Select Answer 1. Determine if b is in W Select Answer A 2. Determine if b is in {aj, az, az } How many vectors are in {aj, a2, az }? (For infinitely many, enter -1) How many vectors are in W? (For infinitely many, enter -...
1 0 -7 3 Let A= 03 -4 and b= Denote the columns of A by a, a, ay, and let W = Span{a,,a,,a3} -26 2 3 a. Is b in {a,,a,,az)? How many vectors are in {a,az.az)? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {a,,a,,az)? Ο Νο Yes How many vectors are in {a,,a,a}? O A. Two OB. Infinitely...
Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote the columns of A by a, a, az, and let W = Span{a.a.az). a. Is b in aa.az)? How many vectors are in a .a .a? b. Is bin W? How many vectors are in W? c. Show that a is in W. (Hint: Row operations are unnecessary.] a. Is b in {a .az.az)? No Yes O How many vectors are in aaa? A....
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
-247 -3 2. Let V1 = 1 , V , and V3 = , let B = (V1, V2, V3), and let W be the subspace spanned -2 by B. Note that B is an orthogonal set. 21 with respect to B, without inverting any matrices or a. [1 point] Find the coordinates of ū= 1: L 6 solving any systems of linear equations. 5 637 10 16. it point Find the sector in We st o b. [1 point]...
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...
-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 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns of A by ay, az, az, and let W= = Span{a,,a,,az}. -34 2 -5 1 a. Is b in {a4, az, az}? How many vectors are in {aq,a2, az}? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {aq, az, az}? No Yes How many vectors...
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2 Q2l+3 Qsl). Then T-5sin (100Q) satisfies: -(A) 0ST<1.
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2...
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