A simple 3 times 2 matrix

Consider the 3 times 2 matrix
 A = left( begin{array}{cc} 3 & 4.5  2 & 1.2  -0.1 & 8.2 end{array}right) .
The matrix can be interpreted as the collection of two column vectors: A = (a_1,a_2), where a_j’s contain the columns of A:
 a_1 = left( begin{array}{c} 3  2  -0.1 end{array}right), ;; a_2 = left( begin{array}{c} 4.5  1.2  8.2 end{array}right), ;;
Geometrically, A represents 2 points in a 3-dimensional space.

Alternatively, we can interpret A as a collection of 3 row vectors in mathbf{R}^2:
 A = left( begin{array}{c} b_1^T  b_2^T  b_3^T end{array}right) ,
where b_i’s, i=1,2,3 contain the rows of A:
 b_1 = left( begin{array}{c} 3  4.5 end{array}right), ;; b_2 = left( begin{array}{c} 2  1.2 end{array}right), ;; b_3 = left( begin{array}{c} -0.1  8.2 end{array}right) .
Geometrically, A represents 3 points in a 2-dimensional space.