5. Complete the proof of the property below by supplying the justification for each step. Let V be a vector space, let u, v and w be elements of V and suppose u + w = v + w. Then u = v. Proof: u + w = v + w (u + w) + (-w) = (v + w) + (-w) u + (w+ -w) = v + (w+ -w) %3D u +0 = v +0 u = 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.