In this problem, if you give decimal answers then give at least three digits of accuracy beyond the decimal.The matrixhas the following complex eigenvalues (give your answer as a comma separated list of complex numbers; use "i" for ✓-1 and feel free to use a computer to solve the relevant quadraticequation):λ = 1.65+1.548386257i, 1.65-1.548386257iSince A has non-real eigenvalues, it is not diagonalizable, but we can find a matrix C =section 5.5 of Lay):C =P =cos(6)A =sin(8)-sin(8)cos(8)[113]1.8Further, we may factor Cas C = XY, where X is a matrix that scales by the positive real numberradians, with —π/2 ≤0 ≤ π/2) isand an invertible matrix P such that A = PCP-¹ (I want you to cook up C, P as inand Y is rotation matrix whose counter-clockwise rotation angle (inThis means that if we let B be the basis for R² consisting of the columns of P, then the B-matrix of A is C. So if we're willing to change our basis for IR², then the linear transformationx Ax really is just rotation followed by scaling!

We are given the matrix A=2-1.41.81.3. As per the question, first we will find the eigenvalues and…

In this problem, if you give decimal answers then give at least three digits of accuracy beyond the decimal. The matrix has the following complex eigenvalues (give your answer as a comma separated list of complex numbers; use T for 1 and feel free to use a computer to solve the relevant quadratic equation): A = 1.65+1.548386257i, 1.65-1.548386257i Since A has non-real eigenvalues, it is not diagonalizable, but we can find a matrix C = section 5.5 of Lay): C= P = A cos(6) sin(8) -sin(8) cos(8) 2 -1.4 1.8 1.3 ]] and an invertible matrix P such that A = PCP-1 (I want you to cook up C, P as in a Further, we may factor Cas C = XY, where X is a matrix that scales by the positive real number radians, with →π/2 ≤ 0 ≤T/2) is and Y is rotation matrix whose counter-clockwise rotation angle (in This means that if we let B be the basis for R² consisting of the columns of P, then the B-matrix of A is C. So if we're willing to change our basis for R², then the linear transformation x →→ Ax really is just rotation followed by scaling!

In this problem, if you give decimal answers then give at least three digits of accuracy beyond the decimal. The matrix has the following complex eigenvalues (give your answer as a comma separated list of complex numbers; use T for 1 and feel free to use a computer to solve the relevant quadratic equation): A = 1.65+1.548386257i, 1.65-1.548386257i Since A has non-real eigenvalues, it is not diagonalizable, but we can find a matrix C = section 5.5 of Lay): C= P = A cos(6) sin(8) -sin(8) cos(8) 2 -1.4 1.8 1.3 ]] and an invertible matrix P such that A = PCP-1 (I want you to cook up C, P as in a Further, we may factor Cas C = XY, where X is a matrix that scales by the positive real number radians, with →π/2 ≤ 0 ≤T/2) is and Y is rotation matrix whose counter-clockwise rotation angle (in This means that if we let B be the basis for R² consisting of the columns of P, then the B-matrix of A is C. So if we're willing to change our basis for R², then the linear transformation x →→ Ax really is just rotation followed by scaling!

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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