I have the following Transformation matrix then I have to find the Kernel for it.
I do that by solving the equation:
.
But when I multiplicy these two matrices I get a 1x1 matrix.
And I know that there ought to be 3 Kernel matrices (from Maple )?
SO what do I do?
I would say that
kerf = span{(-1, 1, 0, 0), (-1, 0, 1, 0), (0, 0, 0, 1)}
is a satisfying answer. Agree?
And another question I have to find a Linear Transformation where U (the amount of 2x2 symmetric matrices where ). But How can I do that when kernel is a 1x1??
Yes
I am confused here. By you mean the space of all symmetric matrices? If so you can always let be the trivial mapping i.e. . Then is certainly a linear transformation.And another question I have to find a Linear Transformation where U (the amount of 2x2 symmetric matrices where ). But How can I do that when kernel is a 1x1??
Is there something missing after "where U"? Where U what? And I don't know what you mean by "kernel is a 1x1". The kernel of any Linear Transformation from vector space A to vector space B is a subspace of A.
Are you required to find a transformation that maps 2 by two matrices to a single number and has "all symmetric matrices" as kernel? (You say "2x2 symmertric matrices where but that is true of all symmetric matrices.)
Well I will try and explain it.
I have this linear transformation . And I have this subspace U (a subspace of ) that is all 2x2 diagonal matrices where .
Then I have to find a linear transformation where the kernel is U.
But U is a 2x2 matrix and a such transformation gives a 1x1 matrix...?
What to do!?