The charactertistic polynomial of the matrix C = is p(x) = x²(x - 1). The matrix has two distinct eigenvalues, A₁ <>₂: A₁ has algebraic multiplicity (AM) -1 6 11 -2 15 -5 -1 7 The dimension of the corresponding eigenspace (GM) is A₂ = has algebraic multiplicity (AM) The dimension of the corresponding eigenspace (GM) is Is the matrix C diagonalizable? (enter YES or NO)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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The charactertistic polynomial of the matrix C
=
is p(x) = x²(x - 1).
The matrix has two distinct eigenvalues, >₁<A₂:
A₁
has algebraic multiplicity (AM)
-1 6
11 -2 15
-5 -1 7
The dimension of the corresponding eigenspace (GM) is
A₂ = has algebraic multiplicity (AM) The dimension of the corresponding eigenspace (GM) is
Is the matrix C diagonalizable? (enter YES or NO)
Transcribed Image Text:The charactertistic polynomial of the matrix C = is p(x) = x²(x - 1). The matrix has two distinct eigenvalues, >₁<A₂: A₁ has algebraic multiplicity (AM) -1 6 11 -2 15 -5 -1 7 The dimension of the corresponding eigenspace (GM) is A₂ = has algebraic multiplicity (AM) The dimension of the corresponding eigenspace (GM) is Is the matrix C diagonalizable? (enter YES or NO)
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