12. The matrix that represents a reflection on the plane 2x – y + z = 0, is given (in the standardbases) by:-11-11(A)3-1 111.(B) It can't be computed with the information given

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Answered: 12. The matrix that represents a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Hi, I need help with this Linear Algebra problem, please. Thank you! :)
4. Determine the 2 x 2 matrix that represents the reflection along the line y = -V3x. Use this matrix to find the image of the points A(2, –2) and B(1, V3).
True or false: If Py and Pw are the n x n orthogonal projection matrices to two orthogonal lines V, WC R", then Py Pw is the zero matrix. O True False
5.C) calculate the determinant
9. Given the bases B = {1+2t, 2+t} and C = {1-t, 2-3t} of P₁. Find the change of coordinates matrix Pc-B from B to C.
2. Let a = 2 ---- X= -2 4 and y = 4 2 (a) Find P, the projection matrix along the span of a. (b) Find proja (x). (c) Find proja (y). 3. Let A be a nonsingular 2 x 2 matrix. (a) Find P, the projection matrix onto C(A). (b) Find C(A) and comment on the result of part (a).
Needed to be solved correctly in 10 minutes in the order to get positive feedback please show me neat and clean work for it by hand solution needed
18.- Define the symmetric matrix corresponding to the following quadratic form: F(x, y, z)= x² + z²-2xy+xz - 2yz
70. Consider the matrix M = (ab) where a and c are real and b may be complex. If M can be diagonalized by a matrix S, then S is:

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12. The matrix that represents a reflection on the plane 2x – y + z = 0, is given (in the standard bases) by: -1 1 -1 1 (A) 3 -1 1 1 1. (B) It can't be computed with the information given