0 i 01 1 0 as a matrix over C, where i = √-1.i0 iFind p₁(x), m₁ (x) and determine if A is diagonalisable. Justify your answer.Let A =Select one:None of the others applyPA(x) = (x + i)(x − i)² but (A + iI3)(A − iI3) = 0 som₁(x) = (x + i)(x - i) which is a product of distinct linear factors, so A is diagonalisable.P₁(x) = (x + i)(x² + √2x + i) which does not factorise further. Since A -I3 it follows that m₁ = PA which is not the product of distinct linearfactors, so A is not diagonalisable.○ P₁(x) = (xi)(x² − x − i) which factorises further as it must over C. These 3 roots are all distinct so m₁ = P₁ is a product of distinct linear factors, so Ais diagonalisable.OP₁(x) = (x − i)(x + i)² but (A − iI3) (A + iI3) ‡ 0 so m₁ = PA which is not a product of distinct linear factors, so A is not diagonalisable.

Eigenvalue: A number is said to be an eigenvalue of a matrix A if there is a non-zero vector xsuch…

0 i 0 Let A = 1 10 as a matrix over C, where i = √√-1. Li 0 i Find p₁(x), m₁(x) and determine if A is diagonalisable. Justify your answer. Select one: O None of the others apply O PA(x) = (x + i)(x − i)² but (A + iI3) (A - iI3) = 0 so m₁(x) = (x + i)(x - i) which is a product of distinct linear factors, so A is diagonalisable. O PA₁(x) = (x + i)(x² + √2x+i) which does not factorise further. Since A -13 it follows that mA = PA which is not the product of distinct linear factors, so A is not diagonalisable. ○ P₁(x) = (xi)(x² - x - i) which factorises further as it must over C. These 3 roots are all distinct so m₁ = PA is a product of distinct linear factors, so A is diagonalisable. O P₁(x) = (xi)(x + i)² but (A − iI3) (A + iI3) #0 so m₁ = PA which is not a product of distinct linear factors, so A is not diagonalisable.

0 i 0 Let A = 1 10 as a matrix over C, where i = √√-1. Li 0 i Find p₁(x), m₁(x) and determine if A is diagonalisable. Justify your answer. Select one: O None of the others apply O PA(x) = (x + i)(x − i)² but (A + iI3) (A - iI3) = 0 so m₁(x) = (x + i)(x - i) which is a product of distinct linear factors, so A is diagonalisable. O PA₁(x) = (x + i)(x² + √2x+i) which does not factorise further. Since A -13 it follows that mA = PA which is not the product of distinct linear factors, so A is not diagonalisable. ○ P₁(x) = (xi)(x² - x - i) which factorises further as it must over C. These 3 roots are all distinct so m₁ = PA is a product of distinct linear factors, so A is diagonalisable. O P₁(x) = (xi)(x + i)² but (A − iI3) (A + iI3) #0 so m₁ = PA which is not a product of distinct linear factors, so A is not diagonalisable.

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 32E

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