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...
8 Let t and s be real numbers and let C = [cij]. Prove (s +t)C = sC+tC. ution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as ar
12 points Let L: R3 → R3 defined by L U2 (1 3 57 rui 1 2||uz. Find ker L and dim ker L. LO 2 3] [u be 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 it the test.
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...
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-
Question 1 Let A 6 b- > [|1 and C 5 -2 3. Calculate the following: 4 0 (a) 2(A - 30) (6) ACT CC A(4b) Only work on your blank sheets of paper. You will submit your work a
It + 3 Solve det - 3 0 0 O for t. t - 4 2 Aphr work on your blank sheets of paper You will sub
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...
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...
1. Let A Idef g h i Given that det(A) 1, find det(B) where You should fully justify your answer 3 marks]