Let V = M2x2 be the vector space of 2 x 2 matrices with real number...
Problem 4. Let GL2(R) be the vector space of 2 x 2 square matrices with usual matrix addition and scalar multiplication, and Wー State the incorrect statement from the following five 1. W is a subspace of GL2(R) with basis 2. W -Ker f, where GL2(R) R is the linear transformation defined by: 3. Given the basis B in option1. coordB( 23(1,2,2) 4. GC2(R)-W + V, where: 5. Given the basis B in option1. coordB( 2 3 (1,2,3) Problem 5....
Can u please answer the question (G) 1. (15 marks total) Consider the real vector space (IR3, +,-) and let W be the subset of R3 consisting of all elements (z, y, z) of R3 for which z t y-z = 0. (Although you do not need to show this, W is a vector subspace of R3, and therefore is itsclf a rcal vector space.) Consider the following vectors in W V2 (0,2,2) V (0,0,0) (a) (2 marks) Determine whether...
be the vector space of all two-by-two real matrices. Is either of these subsets a M2x2 1. Let V subspace of V? Justify ( 2) a The set of matrices such that ad d (a) = -1. The set of all two-by-two matrices with zero determinant (b)
2. Let M2x2(R) be the vector space consisting of 2 x 2 matrices with real entries. Let W M2x2 (R) det (A) 0. Show that W is not a subspace of M2x2(R) A E
Long Answer Question LetV = M2x2, the vector space of 2 x 2 matrices with usual addition and scalar multiplication. Consider the set S = {M1, M2, M3} where M [ {].m=[5_1], 25 = [3 1] 1. (6 marks) Determine whether Sis linearly dependent/independent. 2. (2 marks) What is the dimension of Span(S)? 3. (2 marks) Is S a basis for V? 4. (2 marks) Is S a basis for the space of 2 x 2 upper triangular matrices? Please...
2. On subspaces of C(-1,1) Let V C(-1,1) be the vector space of all continuous real valued functions on on the interval (-1, 1), with usual addition and scalar multiplication. (a) Verify, if the set W-f eV: f(0)-0is a subspace of V or not? (b) Verify, if the set W-Uev f(0) 1 is a subspace of V or not? (c) Verify, if the set W-İfEV:f(x)-0V-2-z is a subspace of V or not? 1b) PrtScn Home FS F6 F7 F8 5
Let n EN Consider the set of n x n symmetric matrices over R with the usual addition and multiplication by a scalar (1.1) Show that this set with the given operations is a vector subspace of Man (6) (12) What is the dimension of this vector subspace? (1.3) Find a basis for the vector space of 2 x 2 symmetric matrices (6) (16)
3. Let V be the subspace of M2x2(R) consisting of all matrices in which the sum of entries on each row is equal to 0. Let W be the subspace of M2x2(R) consisting of all matrices in which the sum of entries on each column is equal to 0. Find a basis of V +W.
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations) Question (7) Consider...