![6] 1. Let A= [ 37 67 3 1 3 , V1 = ( 5 5 3 , V2 = -1 2 0 1-2 a) Is vi an eigenvector of A? If so, find its eigenvalue, If not,](http://img.homeworklib.com/questions/8b3c84e0-b437-11eb-8e5a-b9281569b997.png?x-oss-process=image/resize,w_560)
Homework Answers
![1- 1. Given n = [1 / 1] -- 6-8 1. Given A = 13 7 67 3 1 .3 5 5 3 (a) If possible let d, is the eigenvalue of A and op is the](http://img.homeworklib.com/questions/8bf98270-b437-11eb-bde7-9b11c4a9e0fd.png?x-oss-process=image/resize,w_560)
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3,...
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
Let V1 = (1,2,0)^T, V2 = (2,4,2)^T, and V3 = (0,2,7)T and A = [V1,V2,V3] 5)...
Let V1 = (1,2,0)^T, V2 = (2,4,2)^T, and V3 = (0,2,7)T and A =
[V1,V2,V3]
5) (20 points) Let vi = (1,2,0)T, v2 = (2,4, 2)T and v3 = (0, 2.7)T and A- [v1, v2, v3 a) Find an orthonormal basis for the Col(A) b) Find a QR factorization of A. c) Show that A is symmetric and find the quadratic form whose standard matrix is A
37 Let vi = 0 , V2 = 1, and V3 = 2 . These 3...
37 Let vi = 0 , V2 = 1, and V3 = 2 . These 3 vectors are linearly -1] dependent. Fill in the blanks for c2 and C3 so that the following is a linear dependence relation: Vi + C2 V2 + c3 V3 = 0.
1) Determine if w is in the subspace spanned by v1, v2, v3 2) Are the...
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)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (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
(1 point) Let 1 5 -4 |- Find a basis for A -3 Nul(A)'. 0 -1...
(1 point) Let 1 5 -4 |- Find a basis for A -3 Nul(A)'. 0 -1 A basis is {V1, V2} where Vi = V2 II
Please show the detail, thank you! (1 point) (a) Let -4 -7 -2 -4 V1 =...
Please show the detail, thank you!
(1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
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.
Suppose that A= | 2 0 -2 1 (1 0 0 0 -1 . Find the...
Suppose that A= | 2 0 -2 1 (1 0 0 0 -1 . Find the eigenvectors of A (a) Eigenvector with respect to the smallest eigenvalue: V1 = Preview where ői is a unit vector; (b) Eigenvector with respect to the second smallest eigenvalue: 02 = Preview where v2 is a unit vector; (c) Eigenvector with respect to the bigest eigenvalue: V3 = Preview where Uz is a unit vector. Get help: Video
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.
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
Let V1 = (1,2,0)^T, V2 = (2,4,2)^T, and V3 = (0,2,7)T and A =
[V1,V2,V3]
5) (20 points) Let vi = (1,2,0)T, v2 = (2,4, 2)T and v3 = (0, 2.7)T and A- [v1, v2, v3 a) Find an orthonormal basis for the Col(A) b) Find a QR factorization of A. c) Show that A is symmetric and find the quadratic form whose standard matrix is A
37 Let vi = 0 , V2 = 1, and V3 = 2 . These 3 vectors are linearly -1] dependent. Fill in the blanks for c2 and C3 so that the following is a linear dependence relation: Vi + C2 V2 + c3 V3 = 0.
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)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (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
(1 point) Let 1 5 -4 |- Find a basis for A -3 Nul(A)'. 0 -1 A basis is {V1, V2} where Vi = V2 II
Please show the detail, thank you!
(1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
Suppose that A= | 2 0 -2 1 (1 0 0 0 -1 . Find the eigenvectors of A (a) Eigenvector with respect to the smallest eigenvalue: V1 = Preview where ői is a unit vector; (b) Eigenvector with respect to the second smallest eigenvalue: 02 = Preview where v2 is a unit vector; (c) Eigenvector with respect to the bigest eigenvalue: V3 = Preview where Uz is a unit vector. Get help: Video
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.
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