Chapter 2
SSM: Linear Algebra
Chapter 2 2.1
1. Not a linear transformation, since y2 = x2 + 2 is not linear in our sense. 3. Not linear, since y2 = x1 x3 is nonlinear. 5. By Fact 2.1.2, the three columns of the 2 3 matrix A are T (e1 ), T (e2 ), a
SSM: Linear Algebra
Section 4.1
Chapter 4 4.1
1. Not a subspace since it does not contain the neutral element, that is, the function f (t) = 0, for all t. 3. This subset V is a subspace of P2 : The neutral element f (t) = 0 (for all t) is in V sin
Chapter 3
SSM: Linear Algebra
Chapter 3 3.1
1. Find all x such that Ax = 0: . 1 2. 0 . . . 0 3 4. - . 1 0. 0 , so that x = x = 0. . 1 2 . . 0 0 1.
ker(A) = {0}. 3. Find all x such that Ax = 0; note that all x in R2 satisfy the equation, so that ke