Let V be the subspace of ℝ4 spanned by the columns of the matrix  A=[1 2 3 −2 3 8 5 1 −3 −3 −4 −5 ]  (a) Find a basis of V. (b) What is the dimension of V (c) Extend the basis of V to a basis of ℝ4.

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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.