Lecture Notes For Linear Algebra _verified_

The line $y=2x$ in $\mathbbR^2$ is a subspace. The line $y=2x+1$ (does not contain zero) is NOT.

(\dim(W)) = number of vectors in any basis for (W). Example: Standard basis for (\mathbbR^3): (\mathbfe_1,\mathbfe_2,\mathbfe_3 = (1,0,0),(0,1,0),(0,0,1)), (\dim = 3). lecture notes for linear algebra

This is where many students feel lost. Your lecture notes must slow down and define every term with examples AND non-examples. The line $y=2x$ in $\mathbbR^2$ is a subspace