2) Suppose TE L(V) and ( T – 21)(T – 31)(T – 41) = 0. Suppose 2 is an eigenvalue of T. Prove that A = 2 or 1 = 3 or A = 4. Assume the field of scalars is C, R, or Q.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(b) Explain how you would guess the formula above.
2) Suppose T E L(V) and ( T – 21)(T – 3!)(T – 41) = 0. Suppose a is an eigenvalue of T.
Prove that 1 = 2 or 1 = 3 or 1 = 4. Assume the field of scalars is C,R, or Q.
3) Suppose TE L(V) and T² = I and –1 is not an eigenvalue of T. Prove that T = 1.
Transcribed Image Text:(b) Explain how you would guess the formula above. 2) Suppose T E L(V) and ( T – 21)(T – 3!)(T – 41) = 0. Suppose a is an eigenvalue of T. Prove that 1 = 2 or 1 = 3 or 1 = 4. Assume the field of scalars is C,R, or Q. 3) Suppose TE L(V) and T² = I and –1 is not an eigenvalue of T. Prove that T = 1.
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