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Consider the linear transformation T : M22 → R defined by а T = a + d. d a. Find a basis for ker(T). b. Determine the nullity and rank of T c. Is T one-to-one? Explain your answer. d. Is T onto? Explain your answer.

Consider the linear transformation T : M22 → R defined by а T = a + d. d a. Find a basis for ker(T). b. Determine the nullity and rank of T c. Is T one-to-one? Explain your answer. d. Is T onto? Explain your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the linear transformation T : M22 → R defined by а b T — а +d. d a. Find a basis for ker(T). b. Determine the nullity and rank of T c. Is T one-to-one? Explain your answer. d. Is T onto? Explain your answer.
Transcribed Image Text:Consider the linear transformation T : M22 → R defined by а b T — а +d. d a. Find a basis for ker(T). b. Determine the nullity and rank of T c. Is T one-to-one? Explain your answer. d. Is T onto? Explain your answer.
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