# Lin. Transformation

• Dec 3rd 2007, 08:36 PM
caeder012
Lin. Transformation
Let T be the Lin. Trans. $p_2 \rightarrow p_2$ defined by

$T(at^2+bt+c) = (3a+2c)t + (2b-5c)$

1.) Determine a basis of the kernel of $T$

2.) Determine a basis of the range of $T$

3.) Is $T$ onto? Is $T$ one-to-one? Explain!

....

Well for #3 I know one-to-one has to do w/ range and onto has to do w/ kernel...

Some help?
• Dec 3rd 2007, 08:39 PM
caeder012
Quote:

Originally Posted by caeder012
Let T be the Lin. Trans. $p_2 \rightarrow p_2$ defined by

$T(at^2+bt+c) = (3a+2c)t + (2b-5c)$

1.) Determine a basis of the kernel of $T$

2.) Determine a basis of the range of $T$

3.) Is $T$ onto? Is $T$ one-to-one? Explain!

....

Well for #3 I know one-to-one has to do w/ range and onto has to do w/ kernel...

Some help?

Is the basis of the kernel basis = span{ $-4t^2 + 15t + 6$}

because those coefficients make $(3a+2c) + (2b- 5c) = 0$

And for range.. range = span { $t + 1$}

Hmm..
• Dec 4th 2007, 11:51 AM
caeder012
Quote:

Originally Posted by caeder012
Is the basis of the kernel basis = span{ $-4t^2 + 15t + 6$}

because those coefficients make $(3a+2c) + (2b- 5c) = 0$

And for range.. range = span { $t + 1$}

Hmm..

Anyone have some insight? One of the hardest lin alg problems I've come across.
• Dec 4th 2007, 01:02 PM
TKHunny