In each part, find a basis for the given subspace of R3, and state its dimension. a) The plane 2x − y + z = 0.b) The plane y + z = 0.c) The line x = 3t, y = −t, z = t.d) All vectors of the form (a, b, c), where a = b + c.

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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.