Solution 04 13 2016 at 03 00am EDT 1 2 and 2 1 respectively 1 1 pt Find the matrix A of the linear transformation T from R2 to R2 that rotates any
Solution at am EDT and respectively pt Find the matrix A of the linear transformation T from R
Solution at am EDT and respectively pt Find the matrix A of the
and respectively pt Find the matrix A of the linear transformation T from R to R that rotates any
Solution at am EDT and respectively pt Find the matrix A
of the linear transformation T from R to R that rotates any
Solution at am EDT and respectively pt Find the
Solution at am EDT
(Solution) 04/13/2016 at 03:00am EDT. 1 = 2 and 2 = 1, respectively, 1. (1 pt) Find the matrix A of the linear transformation T from R2 to R2 that rotates any...

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Please provide answers! No work needed. High rating guaranteed! I will also give a big tip if finished by tonight!Darshan Sandhu 51 WeBWorK assignment due : 04/13/2016 at 03:00am EDT. 1. (1 pt) Find the matrix A of the linear transformation T from R 2 to R 2 that rotates any vector through an angle of 150 ? in the counterclockwise direction. A = ± ² . 2. (1 pt) To every linear transformation T from R 2 to R 2 , there is an associated 2 × 2 matrix. Match the following linear transformations with their associated matrix. 1. Re?ection about the line y=x 2. Re?ection about the x -axis 3. Counter-clockwise rotation by ? / 2 radians 4. Clockwise rotation by ? / 2 radians 5. The projection onto the x-axis given by T(x,y)=(x,0) 6. Re?ection about the y-axis A. ³ 1 0 0 0 ´ B. ³ 0 1 1 0 ´ C. ³ - 1 0 0 1 ´ D. ³ 1 0 0 - 1 ´ E. ³ 0 1 - 1 0 ´ F. ³ 0 - 1 1 0 ´ G. None of the above 3. (1 pt) Let T : R 2 ? R 2 be the linear transformation that ?rst rotates points clockwise through 30 ? and then re?ects points through the line y = x . Find the standard matrix A for T . A = ± ² . 4. (1 pt) Find the characteristic polynomial of the matrix A = ? ? -4 3 0 0 -5 5 -2 2 0 ? ? . p ( x ) = . 5. (1 pt) If v 1 = ± -5 -3 ² and v 2 = ± -5 -4 ² are eigenvectors of a matrix A corresponding to the eigenvalues ? 1 = - 2 and ? 2 = - 1, respectively, then A ( v 1 + v 2 ) = ± ² and A ( - 3 v 1 ) = ± ² . 6. (1 pt) Find a basis of the eigenspace associated with the eigenvalue 1 of the matrix A = ? ? ? ? -1 0 4 0 -2 1 3 1 -1 0 3 0 -1 0 3 0 ? ? ? ? . ? ? ? ? ? ? ? ? , ? ? ? ? ? ? ? ? 7. (1 pt) The matrix A = ? ? -6 6 12 -3 3 6 -3 3 6 ? ? has two real eigenvalues, one of multiplicity 1 and one of mul- tiplicity 2. Find the eigenvalues and a basis of each eigenspace. ? 1 = has multiplicity 1, Basis: ? ? ? ? , ? 2 = has multiplicity 2, Basis: ? ? ? ? , ? ? ? ? . 8. (1 pt) Let A = ± -53 36 -72 49 ² . Find an invertible matrix P and a diagonal matrix D such that PDP - 1 = A . P = ± ² D = ± ² 9. (1 pt) Let A = ? ? 3 0 0 0 3 0 12 12 -1 ? ? . Find an invert- ible matrix P and a diagonal matrix D such that D = P - 1 AP . P = ? ? ? ? D = ? ? ? ? 10. (1 pt) Let M = ± 1 -2 4 7 ² . Find formulas for the entries of M n , where n is a positive inte- ger. M n = ± ² . Generated by the WeBWorK system c ± WeBWorK Team, Department of Mathematics, University of Rochester 1

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