18 points Save Answer 3) Use the Gram-Schmidt process to transform the basis 00€ for the Euclidean space Rº with the standard inner product into an orthogonal basis for R3. Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after you submit the test. TT TT Paragraph Arial 3 (12pt) - E-T-- 15 points Save Ans 4) Find the standard...
15 points Save Ar 4) Find the standard matrix representing each given linear transformation. a) L: R3 R2 defined by L u2 4u U3 Find the standard matrix representing L. U1 0 b) L:R2 R3 defined by z ([,]) Find the standard matrix representing L. c) Find L(() using the standard matrix and linear transformation in part b. Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will...
2) Let V = R2 and let u = 11 points Save Answer and v= Cl be vectors in R2. Define (u, v) = 2uv - 4 U2 - uzv. + 6u2V2. a) Find (u, v) where u = Lola and v= = [1 b) Determine the length of v in the inner produce space. c) Determine real number a such that u and v are orthogonal. Do not type your solution (work and answer) in the textbox below. Only...
Let L:R4 → R3 be a linear operator defined by: ui U2 L ( U1 + U3 U2 + U3 U2 + 4 U3 14 What is dim(Range(L))? Answer:
xt yt z=2 Solve the system using Gaussian Elimination or Gauss-Jordan reduction. 6x - 4y + 5z = 31 5x + 2y + 2z = 13 3 points Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after you submit the test. Τ Τ Τ Τ Paragraph Arial 3 (12pt) ET TT, S % DOQ CHE n 4 Question 4...
16 points Save Diagonalize the matrix A = and find an orthogonal matrix P such that P-1AP is diagonal. ot type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after submit the test. TTT Paragraph v Arial 3 (12pt) EE. T-
Let L: R3 --> R3 be defined by Only need c-e solved. 6, (24 points) Let L : R3 → R3 be defined by (a) Find A, the standard matrix representation of f (b) Let 0 -2 2. Check that倔,G, u) is a basis of R3. (c) Find the transition matrix B from the ordered basis U (t, iz, a) to the standard basis {e, е,6). For questions (d) and (e), you can write your answer in terms of A...
#12 6.3.20 s Question Help 5 0 Let un 2. u2 -8 and uz = 1 Note that u, and uz are orthogonal. It can be shown that ug is not in the subspace W spanned by u, and up. Use this to - 1 0 construct a nonzero vector v in R3 that is orthogonal to u, and up. 4 The nonzero vector v = is orthogonal to u, and u2
#8 6.3.15 6 -3 -2 Let y = u- U2 - 1 Find the distance from y to the plane in R3 spanned by u, and uz: 3 1 -2 The distance is (Type an exact answer, using radicals as needed.)
7) Find a basis for the range(L). Find the Ker(L). Let L: R3 → R be defined by 1 0 1 L 2 2 1 3 111 111 B)-1 B 13