Question: (a) If T: R3 R3 is a linear operator, and if the kernel of T is a line through the origin, then what kind

(a) If T: R3 → R3 is a linear operator, and if the kernel of T is a line through the origin, then what kind of geometric object is the range of T? Explain your reasoning.
(b) If T: R3 → R3 is a linear operator, and if the range of T is a plane through the origin, then what kind of geometric object is the kernel of T? Explain your reasoning.

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