Consider P4 be a set of all the point on a plane through the origin in R4. The general equation of a plane through the origin in R4 is as follow: aw + bx + cy + dz = 0, where a, b, c, and d are fixed constant and at least one is not zero. Show that P4 with the standard addition and scalar multiplication is a vector space.

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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.