Homework Statement
let T: R^4 --->R^3, where T(v)=A(v) and matrix A is defined by
A = [2 1 -1 1
1 2 0 5
4 -1 1 0
Find kernel of T, nullity of T, range of T and rank of T
Homework Equations
The Attempt at a Solution
ok. ker(T) = Null(A)...
it would be better, but none is given. do you know how i can figure out y_0?
i have h = .4 from b-a/n 1--1/5 = .4
once i have y_0 i can finish the problem, this is what i need help with.
thats what I am trying to do too. actually the instructions say to show work for the iterations, so do u know how i can start? once i get started, i should be able to finish it
thats the thing...i went to two different professors today and asked for help, one of which was the author of the book. he said its solveable and that you don't need an initial condition to solve, and another professor said that you do, because you can have so many different solutions on that x...
sorry bout the bump...
no...c1 or c2 must be zero to satisfy those equations, which would make them linearly independant?
pls tell me if next part is right...
if i say that 2c_1 - c2 = x1 and -c1+c2 = x2...since this tells me how to get c's...this set spans R^2, thus forming a basis?
Homework Statement
show that
\left(\begin{array}{cc}2 & -1\\-1 & 1\end{array}\right)
forms a basis for R^2Homework Equations
The Attempt at a Solution
ok...my instructor said he wants me to show that they are linearly independant and to show that they span to form a basis...not just by a...
the exact problem is 1) apply runge kutta of 4th order to solve the ode on [-1,1] with n = 5
(e^x+y)dx-dy=0
were i got x_0 is -1 is from my notes that said x_0 = a.
in my notes it says that y(x_0) = y_0
im pretty sure my x_0 is right but i don't know how to get y_0
Homework Statement
apply the runge kutta of order 4 to solve the ode on [-1,1] with n = 5 of
(e^x+y)dx-dy=0
Homework Equations
The Attempt at a Solution
the problems i have done so far gave me an initial condition to find the k values, then to plus them into the formula...i...