My situation is pretty similar to yours. I am 32 and 3 classes away from an undergraduate degree in math. My plan of action is to job hunt and continue to take classes after graduation in order to make myself more competitive for entrance to grad school. I am interning this summer in...
Homework Statement
if given the general solution to a differential equation
y(t)=a cos t + b sin t + ((cos wt)/1-w^2),
Find out how long it takes the solution to approach the steady state solution.
original second order differential equation:
y'' + y = cos wt such that 0 < w < 10...
Theorem 9
Let T: R^n → R^n be a linear transformation and let A be the standard matrix for T. Then T is invertible if and only if A is an invertible matrix. In that case, the linear transformation S given by S(x) = A^-1 x is the unique function satisfying
(1) S(T(x)) = x for all x in R^n
(2)...
Homework Statement
Let T be a linear transformation that maps Rn onto Rn.
Show that T-1 exists and maps Rn onto Rn.
Is T-1 also one to one?
Homework Equations
The Attempt at a Solution
I am not quite sure where to start. To prove that T is invertible I need to show that A is an...