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...
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.
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-
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...
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...
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
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...
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...
question 3 (b)
Problem #3: Let R4 have the inner product <u, v>-#1v1 + 2112v2 + 31/3V3 + 414V4 (a) Let w (0, 6, 3,-1). Find |w (b) Let Wbe the subspace spanned by the vectors u (0, 0, 2,1), and u2-,0,,-1) Use the Gram-Schmidt components of the vector v2 into the answer box below, separated with commas process to transform the basis fui. u2 into an orthonormal basis fvi, v23. Enter the Enter your answer symbolically as in these...
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B 1 (a) via reduction to triangular form (b) by cofactor expansion swer) in the textbox below. Only work on your blank sheets of paper. You will submit your 3 (12pt) - T-