MATH 2574H Lecture Notes - Gaussian Elimination, Vector Space, Linear Independence

• School: UMN
• Department: Mathematics
• Course: MATH 2574H
• Professor: Jasmine Foo

Document Summary

Calciv page 1 row reduce thissystem will be consistent no matter what you need to put variables for theseinfinitely many solutions linearly independent. There are more columns than rowsnot linearly independent. [0 0] is a solution but if matrix is invertible (and this one is since determinant isn"t 0it"s 2) is the only solutionso the given 2 vectors are linearly independent. Let"s say we have intvertible matrix w/ column vectors. Vector space of polynomials of degree <= 2. Suppose we have p(x), q(x) (p(x) = a + bx + cx2: p(x) + q(x) is a polynomial degree <= 2, dp(x) = da + dbx + dcx2 is in p2. Calciv page 3: dp(x) = da + dbx + dcx2 is in p2. No, b/c 1st one doesn"t have a constant, 2nd one doesn"t have squared term. Check if f(x) and g(x) are differentiable: is f(x) + g(x) differentiable? yes b/c (f(x) + g(x))" = f"(x) + g"(x, (cf(x))" = cf"(x)works.