Let F be the vector space of infinitely differentiable functions from R to R. Consider the subspace: W = span{e^t, sin(2t), cos(3t)} 1. Show that the three vectors above are linearly independent. Consider the linear operator T: W–>W T(f) = f"(t) – af(t) = ( - al) (f). || | dt2 For which real values of a is T invertible 2.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.