2. Compute the minimal polynomial of the following matrix (with coefficients in R) WITHOUT comput- ing the characteristic polynomial: -10 3 3 M:=-18 5 6 -18 6 5, Hint. Solve the system of linear equations M² + a - M + b.id3 = 0 for a, bE Q and justify that this %3D gives the minimal polynomial.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 46E
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2. Compute the minimal polynomial of the following matrix (with coefficients in R) WITHOUT comput-
ing the characteristic polynomial:
-10 3 3
M:=
-18 5 6
-18 6 5,
Hint. Solve the system of linear equations M2 + a - M + b. idz = 0 for a, b e Q and justify that this
gives the minimal polynomial.
Transcribed Image Text:2. Compute the minimal polynomial of the following matrix (with coefficients in R) WITHOUT comput- ing the characteristic polynomial: -10 3 3 M:= -18 5 6 -18 6 5, Hint. Solve the system of linear equations M2 + a - M + b. idz = 0 for a, b e Q and justify that this gives the minimal polynomial.
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