2. Find the domain, codomain, kernel and range, rank and nullity, of the following linear transformations:...

 

Transcribed Image Text:

2. Find the domain, codomain, kernel and range, rank and nullity, of the following linear transformations: (a) [6 pts] D: P2 → P₁ given by derivative. For example, D(3x² – 2x + 1) = 6x − 2. (b) [2 pts] D: P2 → P11 given by derivative. (c) [6 pts] T: P2 → R² defined by T(p(x)) = (p(0), p(1)). For example, T(3x² - 2x+1) (1, 2). = (d) [6 pts] T: M2x2 → P2 defined by T(ab) = cx² + bx + a + d. For example, T(¹2) = 3x² + 2x + 5. 2. Find the domain, codomain, kernel and range, rank and nullity, of the following linear transformations: (a) [6 pts] D: P2 → P₁ given by derivative. For example, D(3x² – 2x + 1) = 6x − 2. (b) [2 pts] D: P2 → P11 given by derivative. (c) [6 pts] T: P2 → R² defined by T(p(x)) = (p(0), p(1)). For example, T(3x² - 2x+1) (1, 2). = (d) [6 pts] T: M2x2 → P2 defined by T(ab) = cx² + bx + a + d. For example, T(¹2) = 3x² + 2x + 5.