1 Question 3 (4 Marks) show key steps Consider the vector space M2x2(C). i Let Z...
Consider the vector space P3 (R). Let Z = Span ({1 – x + x2 23,1 + 2x + 3x2 + 4x3, x + x3}). Is 6+ 7x + 8x2 + 9x3 E Z? . Consider the vector space M2x2(C). 1 1 i ({( 2+3 );( 1+i 2 );( )}) 3i 2 + 2i 3 + 3i Let Z Span 2 + 3i 2 – 31 2i -2i Is -1+i EZ? 10 + 112 )
Question 2 (4 Marks) show key steps Consider the vector space P3 (R). Let Z = Span({1 - 2+x2 – 2), 1 + 2x + 3x2 + 4x®, x + x®}). Is 6+ 7+ + 8x2 + 9x3 EZ?
Question 7 (6 marks) Consider M2x2 equipped with the inner product Let S c M2x2 be the subspace spanned by [1 21 [0 1 (a) Find an orthonormal basis for S (b) Find the element of S closest to 0 1
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...
(Functional analysis) Let C be the space of all functions having Question 4. (3 marks) Let C([0, 1]) be the space of all functions having continuous derivative For each fe C(0,1), set 1/2 1 0 Show that I-1l is a norm of the space of C (0, 1) Question 4. (3 marks) Let C([0, 1]) be the space of all functions having continuous derivative For each fe C(0,1), set 1/2 1 0 Show that I-1l is a norm of the...
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...
3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V + V be the linear operator defined by T(A) -1 (i) Compute T:((1+i :)) (ii) Determine whether or not there is an orthonormal basis of eigenvectors 8 for which [T], is diagonal. If such a basis exists, find one.
3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V → V be the linear operator defined by 0 T(1) = ( ; ;) A. (i) Compute To((.) (ii) Determine whether or not there is an orthonormal basis of eigenvectors B for which [T]is diagonal. If such a basis exists, find one.
Let V = M2x2 be the vector space of 2 x 2 matrices with real number entries, usual addition and scalar multiplication. Which of the following subsets form a subspace of V? The subset of upper triangular matrices. The subset of all matrices 0b The subset of invertible matrices. The subset of symmetric matrices. Question 6 The set S = {V1, V2,v;} where vi = (-1,1,1), v2 = (1,-1,1), V3 = (1,1,-1) is a basis for R3. The vector w...
Part 2 please !! 3. Consider the inner product space V = M2x2(C) with the Frobenius inner product, and let T:V + V be the linear operator defined by T(4) = ( ; A. (i) Compute "((1+i (ii) Determine whether or not there is an orthonormal basis of eigenvectors 8 for which (T), is diagonal. If such a basis exists, find one.