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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