Math Help - Lin. Transformation

Let T be the Lin. Trans. defined by



1.) Determine a basis of the kernel of

2.) Determine a basis of the range of

3.) Is onto? Is 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?

Originally Posted by caeder012

Let T be the Lin. Trans. defined by



1.) Determine a basis of the kernel of

2.) Determine a basis of the range of

3.) Is onto? Is 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{ }

because those coefficients make

And for range.. range = span { }

Hmm..

Originally Posted by caeder012

Is the basis of the kernel basis = span{ }

because those coefficients make

And for range.. range = span { }

Hmm..

Anyone have some insight? One of the hardest lin alg problems I've come across.

Shouldn't you be thinking about:

3a + 2c = 0

AND

2b - 5c = 0

????

You certainly found one solution to this over-defined system. What about the infinitely many others?

May 'a' be zero (0)?