It is amazing the difference a space will make. :biggrin:
Thank you so much!...I was able to do all parts of the problem and even presented them in class!
Homework Statement
Let f: A \rightarrow B be given and let {X_{\alpha}} for \alpha \in I be an indexed family of subsets of A.
Prove:
a) f(U_{\alpha\inI} X_{\alpha}) = U_{\alpha\inI}f(X_{\alpha})
The Attempt at a Solution
To prove these two things are equal I must show...
[SOLVED] Linear Algebra - Direct Sums
Homework Statement
Let W1, W2, K1, K2,..., Kp, M1, M2,..., Mq be subspaces of a vector space V such that
W1 = K1 \oplusK2\oplus ... \oplusKp
and
W2 = M1 \oplusM2 \oplus...\oplusMq
Prove that if W1 \capW2 = {0}, then W1 + W2 = W1 \oplusW2 = K1...
[SOLVED] linear algebra determinant of linear operator
Homework Statement
Let T be a linear operator on a finite-dimensional vector space V.
Define the determinant of T as: det(T)=det([T]β) where β is any ordered basis for V.
Prove that for any scalar λ and any ordered basis β for V...
[SOLVED] Prove A is Diagonalizable (Actual Question)
Homework Statement
Suppose that A \in M^{nxn}(F) and has two distinct eigenvalues, \lambda_{1} and \lambda_{2}, and that dim(E(subscript \lambda_{1} ))= n-1. Prove that A is diagonalizable.
The Attempt at a Solution
So far, I...
[SOLVED] Linear Algebra Dual Basis
Let V= R3 and define f1, f2, f3 in V* as follows:
f1 = x -2y
f2 = x + y +z
f3 = y -3z
part (a): prove that {f1, f2, f3} is a basis for V*
I did this by using the gauss jordan method and showing that {f1, f2, f3} is linearly independent. Now...