I am not sure where to start on this linear algebra question. The set of vectors for part a is these ones: 216 131 6. (a) [2] Is the set of vectors in Question 5 (b) a spanning set for R3? (b) [5] Let 01 U2 and vz Find (with justification) a vector w R4 such that w¢ Span何,v2, v3} (c) [3 In (b), is the set {oi,T2, T, a basis for R4? Justify your answer.
Problem 4 A set of vectors is given by S = {V1, V2, V3} in R3 where eV1 = 1 5 -4 7 eV2 = 3 . eV3 = 11 -6 10 a) [3 pts) Show that S is a basis for R3. b) (4 pts] Using the above coordinate vectors, find the base transition matrix eTs from the basis S to the standard basis e. Then compute the base transition matrix sTe from the standard basis e to the...
2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector v in the orthogonal complement of the space 0 Span 2,2 Do not simply compute the cross product. (c) Let A be a 5 × 2 rnatrix with linearly independent columns. Using the rank-nullity theorem applied to AT, and any other results from the course, find the dinension of Col(A) 2. (a) Show that is an orthogonal basis for R3. (b) Find a non-zero vector...
QUESTION 2 Consider the vector space R3 (2.1) Show that (12) ((a, b, c), (x, v, z))-at +by +(b+ c)(y + z) is an inner product on R3 (2.2) Apply the Gram-Schmıdt process to the following subset of R3 (12) to find an orthogonal basis wth respect to the inner product defilned in question 2.1 for the span of this subset (2.3) Fınd all vectors (a, b, c) E R3 whuch are orthogonal to (1,0, 1) wnth respect to the...
Q2. Consider the matrix A 6 3 0 -1 0-2 0 5 (a) Find all eigenvalues of the matrix A. (b) Find all eigenvectors of the matrix A. (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R3? (Justify your answer
(a) In the vector space, V = {f : R → R}, prove that the set {x9,sin5x,cos2x} is linearly independent. (b) Is {(1,2,3),(−2,1,0),(1,0,1)} a basis for R3? Justify your answer.
9. Consider the set A 2 kEN) ,2,4, 8, 16,...) a. Give a recursive definition of the set A. Be sure to clearly indicate which part of the definition is the basis and which is the recursion b. Use your definition to show that A is closed with respect to multiplication 9. Consider the set A 2 kEN) ,2,4, 8, 16,...) a. Give a recursive definition of the set A. Be sure to clearly indicate which part of the definition...
solve it clear please ????? 6 0 0 1 Q2. Consider the matrix A = 2 -5 -6 -50 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R$? (Justify your answer) (5 pts) Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is:...
1. Consider the following two bases for R3. --{():(1) 0)) -= {(8) 0) (1) and (a) Compute Ps-B where S is the standard basis for R. (b) Compute PB-B!. (c) Compute PB:~B. (d) Fill in the blanks. Do your computations on scrap paper. -) (1) (-3, 1, 2), = ( —, - (ii) (1, -1, 0 )B= ( -_- (iii) (0, 3, -1 ),= (-
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...