In each of the following bullet points, you are given a linear operator and some information about the operator. In each case, indicate which of the following options (a)-(c) is true about that linear operator. (Note: It's possible for the options (a)-(c) to be used more than once or not at all.) (a) this linear operator is definitely diagonalizable (b) this linear operator might be diagonalizable (c) this linear operator is definitely not diagonalizable T1: R³ → R³ has exactly three distinct eigenvalues. [ Select ] • T2 : R³ → R³ has exactly two distinct eigenvalues. [ Select ] • T3 : P3 (R) → P3 (R) has exactly one distinct eigenvalue. [ Select ]
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![In each of the following bullet points, you are given a linear operator and some information about the operator.
In each case, indicate which of the following options (a)-(c) is true about that linear operator. (Note: It's possible
for the options (a)-(c) to be used more than once or not at all.)
(a) this linear operator is definitely diagonalizable
(b) this linear operator might be diagonalizable
(c) this linear operator is definitely not diagonalizable
T1 : R° → R has exactly three distinct eigenvalues. [ Select ]
T2 : R³ → R³ has exactly two distinct eigenvalues. [ Select ]
T3 : P3 (R) – P3(R) has exactly one distinct eigenvalue. [ Select ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4798b99-57d8-49c4-99f2-a0d10bf3740f%2F3e2b20c2-56e6-40db-815d-2f1069418bf1%2Fa1v2by_processed.png&w=3840&q=75)
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