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phrygian
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Homework Statement
(124) If a linear transformation T : R3 -> R5 is one-to-one, then
(a) Its rank is five and its nullity is two.
(b) Its rank and nullity can be any pair of non-negative numbers that add
up to five.
(c) Its rank is three and its nullity is two.
(d) Its rank is two and its nullity is three.
(e) Its rank is three and its nullity is zero.
(f) Its rank and nullity can be any pair of non-negative numbers that add
up to three.
(g) The situation is impossible.
(125) If a linear transformation T : R3 -> R5 is onto, then
(a) Its rank is five and its nullity is two.
(b) Its rank is two and its nullity is three.
(c) Its rank is three and its nullity is zero.
(d) Its rank and nullity can be any pair of non-negative numbers that add
up to three.
(e) Its rank is three and its nullity is two.
(f) Its rank and nullity can be any pair of non-negative numbers that add
up to five.
(g) The situation is impossible.
Homework Equations
The Attempt at a Solution
These two problems on my practice test have me completely stumped, could someone help shed some light?
I understand the definitions of onto and one-to-one, but don't understnad how to connect this to the null space of a linear transformation from Rm to Rn?