Consider the functions fi(x) = 6x, f2(x) = 3x², and f3(x) = 12x + 3x². A) If fi and f2 are solutions of the DE x²y" – 2xy' + 2y = 0, show that f3(x) is also a solution for the DE. B) Use the Wronskian to show that fi,f2 and f3 are linearly dependent on the interval (-0, 0).

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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.