Consider the vector space R 4 over the field of real numbers F = R 4. Let W = { ha, b, c, di | where a - 2d = 0 and a, b, c, d are real numbers } Show that W is a subspace of R * .

Q: Give a counter example to show that W is not subspace of R3. W=set of (x, y, z) where x + y = 1

A:

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.