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Linear Algebra With Applications
Found in: Page 120
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

What is the image of a function f from to given by

f(t)=t3+at2+bt+c ,

where a,b,c are arbitrary scalars?

The image is (f) =ft=t3+at2+bt+c: t in T ,image is all of .

See the step by step solution

Step by Step Solution

Step 1: Consider the parameters.

The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

image(f)=fx: in X =b in Y : b=f(x),for some x in X

The Kernel of the transformation results in ft=t3+at2+bt+c:t in T , as the reflection is its own inverse.

As the inverse of the reflection exists thus, the image will be . The kernel is of dimension image(f)=f(t)=t3+at2+bt=c:t in T so, the image will be of .

Step 2: Final answer.

The image is image(f)=f(t)=t3+at2+bt+c:t in T , image is all of .

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