MAT3701 Assignment 2 Semester 1 2026 - Due 5 June 2026

MAT3701 Assignment 2 Semester 1 2026 – Due 5 June 2026

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MAT3701 Assignment 2 Semester 1 2026 – Due 5 June 2026

MAT3701 ASSIGNMENT 2 2026
DUE 5 JUNE 2026
Question 1 (20 marks)
(1.1) Consider the transformation
T : P2(R) → P3(R)
′
f(x) 7→ xf(x) + f
(x).
Question 1
(1.1.1) Prove that
T
Let
f , g ∈ P

(R)
and
c ∈ R
.
2
T (f + g) = x(f + g)(x) + (f + g) (x)
′
′
= x[f (x) + g(x)] + [f (x) + g (x)]
′
′

= xf (x) + xg(x) + f (x) + g (x)
′
′
= [xf (x) + f (x)] + [xg(x) + g (x)]
′
= T (f ) + T (g).

is linear.

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