2. Consider the following system of equations expressed in matrix-vector form: 3 -1 -1 5 = (+09-0 -12 4 -2-1 A I The eigenvalue decomposition (EVD) of A is given by A = QDQ¹ where G 1 3 20 1 0 -1 −1 2 D = 0 1 0 , 2 7 2 0 0 -1 Q = Using the EVD of A, we have Ax=6 ⇒ QDQ¹=b ⇒ DQ¯¹ñ = Q¯¹b. Let = Q¹ and y = Q-¹b, which implies = Q and Q = b. Thus A 6 D= y. Use the EVD of A to solve the system of equations Ax = b in the following steps: (a) Solve for such that Q = b. (b) Solve for such that Dz = y. (c) Compute = Qz.

2. Consider the following system of equations expressed in matrix-vector form: 3 -1 -1 5 = (+09-0 -12 4 -2-1 A I The eigenvalue decomposition (EVD) of A is given by A = QDQ¹ where G 1 3 20 1 0 -1 −1 2 D = 0 1 0 , 2 7 2 0 0 -1 Q = Using the EVD of A, we have Ax=6 ⇒ QDQ¹=b ⇒ DQ¯¹ñ = Q¯¹b. Let = Q¹ and y = Q-¹b, which implies = Q and Q = b. Thus A 6 D= y. Use the EVD of A to solve the system of equations Ax = b in the following steps: (a) Solve for such that Q = b. (b) Solve for such that Dz = y. (c) Compute = Qz.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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