Lecture 2: 1.3–1.5: Vectors, geometry of ℝⁿ, and solution sets

Column Vectors

A column vector is a matrix with one column.

Examples:

u=[[2],[1]],[[−2],[0]]∈R^2,[1.5]∈R

The Real Numbers and ℝ^n

• ℝ^n: the set of all real numbers

• ℝ^n: the set of all vectors with n real entries

R^n={v=[[(v_1)],[(v_2)],[⋮],[(v_n)]]*(∣_^)((v_1)),…,(v_n)∈R}

Examples:

[[2],[1]]∈R^2,[[2],[1],[0]]∈R^3