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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2. The Stretching Problem Imagine a linear transformation T: R² →R² that has the following properties: In the direction along the line y = -3x, the transformation stretches all points by a factor of two. In the direction along the line y = x, the transformation keeps all points fixed. 2a).Use the space on the right to sketch what should happen to the image shown on the left when it is stretched according to the transformation described above. You may use a combination of intuition or calculations, as well as any additional sketches below or on your group's whiteboard. IN
7. (a) Find the equation of the straight line y = ao + a₁t which best fits the following points: 12 13 4 t y 1 3 4 2 2 3 (b) Find the projection matrix onto C(A), the column space of A, where A = 1 1 1 2 1
5: Let W be the plane with the equation 6x -y + 5z = 0. Find the standard matrix P for the orthogonal projection onto W. Use the following formula = A(4"A)\A", P = where the matrix A is constructed using any basis for W as its column vectors. Enter the first row of the matrix P (in order) into the answer box below, separated with commas. i.e.., enter the values p11, p12- P13.
2. Let A = be an orthogonal 2 × 2 matrix. cos(0) sin(0 (a) Explain why the vector can be written as for some value of 0. a Use your answer to part (a) to find all 2×2 orthogonal matrices A = |C (b) (Hint: What can the second column of A look like?) (c) det(A) = 1? What kind of linear transformation do they correspond to? ! Given your answer to part (b), what are the 2 × 2 orthogonal matrices with

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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