Question

Consider the operation on p2 that takes ax^2+bx+c to cx^2+bx+a . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix? (b) Consider the operation on p3 that takesax^3+bx^2+cx+d to cx^3-bx^2-ax+d . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix?

Answer 1

To prove a given map is a linear transformation you must verify that it satisfies the properties of a linear transformation.

Answer 2

but how sir and on which polynomial

Answer 3

can you solve sir part b of question

Answer 4

First of all what is the dimension of P^2?

Answer 5

not mentioned in question

Answer 6

There is a bijection from any vector space to F^n or in this case R^n

Answer 7

The idea is that any linear transformation expressed in an arbitrary vector space can be rewritten as a linear transformation in F^n

Answer 8

Start with a standard basis for P^2
\[\{1, x, x^2\}\]

Answer 9

i did not get your point please help

Answer 10

T(a,b, c) = (c, b, a)
Is equivalent to the transformation in the polynomial space.

Answer 11

what about part b and what is matrix obtained

Answer 12

A matrix is written by transforming a set of basis vectors and writing their image as a linear combination of a basis in the target space.

Answer 13

what will be answer

Answer 14

T(1, 0, 0) = (0, 0, 1)
T(0, 1, 0) = (0, 1, 0)
T(0, 0, 1) = (1, 0, 0)

\[\left[\begin{matrix}0 & 0 & 1\\ 0 & 1 & 0 \\ 1 & 0 & 0\end{matrix}\right]\]

Answer 15

Part B is no, P3 is 4 dimensional

Answer 16

(Part B is no, P3 is 4 dimensional) what it means