Maiclubk

2021-03-02

Let T $P}_{2}\to {\mathbb{R}}^{3$ be a transformation given by

$T\left(f\left(x\right)\right)=\left[\begin{array}{c}f\left(0\right)\\ f\left(1\right)\\ 2f\left(1\right)\end{array}\right]$

(a)Then show that T is a linear transformation.

(b)Find and describe the kernel(null space) of T i.e Ker(T) and range of T.

(c)Show that T is one-to-one.

(a)Then show that T is a linear transformation.

(b)Find and describe the kernel(null space) of T i.e Ker(T) and range of T.

(c)Show that T is one-to-one.

Elberte

Skilled2021-03-03Added 95 answers

The map T :

(a)Let f,

Therefore T:

(b)

Therefore Nullity

Again Range(T)

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