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15 points Save Ar 4) Find the standard matrix representing each given linear transformation. a) L:...
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-
Q4. Let L: R2 + Rº be a transformation defined by L (0-2 [3u2 – U1 U1 – U2 -502 (a) Show that I is a linear transformation. (b) Find the standard matrix A of L, and find L ([31]) using the matrix A. (c) Do you think that any transformation T:R2 + R² is linear? (Justify your answer).
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 : R2 → R3 be a linear transformation such that L 1 1 = 1 2
3 and L 1 2 = 2 1 3 . Find L 2 1 Find the standard matrix
representing L. Find the dimensions of the kernel and the range of
L and their bases.
12. Let L : R² + RP be a linear transformation such that L | (3) - -(5)-(1) Find I (*) Find the standard matrix representing L. Find...
AB matrix, linear operator R2 into R3 find the standard fro 11) For the linear operator L(x1, 22, ^1 + 22
AB matrix, linear operator R2 into R3 find the standard fro 11) For the linear operator L(x1, 22, ^1 + 22
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2
Assume that T is a linear transformation. Find the standard matrix of T T R3-R2 T (el) : (19), and T (e2): (-6,4), and T (e)-9-7), where el e2 and e3 are the columns of the 3x3 identity matrix A(Type an integer or decimal for each matrix element.)
Assume that T is a linear transformation. Find the standard
matrix of T...
Assume that T is a linear transformation. Find the standard matrix of T 2T radians T: R2 R2, rotates points (about the origin) through 3 A = (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed.)