Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R, (b) Let and 0 represent the functions e2", xe2a and x?e2a, respectively. 3 For example, 4 represents 3e2a + 4xe2a + 5x²e2«. Find the matrix of differentiation as a linear transformation on V.

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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.