(a) Let V be a finite dimensional inner product vector space, U a subspace of V . Show that there exists a subspace W of V such that V = U ⊕ W. b) Let V = P4(Z5). Find a basis for the subspace spanned by 1 + 2x + x^2, 1+ x + x^2, 2 + x, 1 +3x, 1 + x^2, x^3 from this set of vectors.

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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.