Download Homework 17

Homework 17
For the following three problems, determine whether or not the indicated
set of matrices is a subspace of M33 .
1. The set of all diagonal 3 3 matrices.
2. The set of all nonsingular 3 3 matrices.
3. The set of all singular 3 3 matrices.
For the following two problems, determine whether or not each indicated set
of functions is a subspace of the space F of all real-valued functions on R.
4. The set of all f such that f (x) 6= 0 for all x.
5. The set of all f such that f ( x) = f (x) for all x.
For the following two problems, determine whether the given functions are
linearly independent.
6.
7.
f1(x) = sin x, f2(x) = cos x
f1(x) = ex, f2(x) = xex
For the following problem, nd a basis for the two-dimensional solution space
of the given dierential equation. Hint: First let v(x) = y (x) and solve for v,
then integrate to nd y.
0
8.
y
00
5y = 0
1