Chapter 2.3

Class 7

Find an example
(a) Four distinct nonzero vectors that span $R^3$
(a) Four distinct nonzero vectors that span $R^4$
(a) Four distinct nonzero vectors that do not span $R^3$
(a) Four distinct nonzero vectors that do not span $R^4$


Sample solution:

(b) $ \begin{bmatrix} 1 & 0 & 0 & 0 \\
0 & 1 &0 & 0 \\
0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1 \end{bmatrix} $

(d) $ \begin{bmatrix} 1 & 2 & 3 & 4 \\
0 & 0 &0 & 0 \\
0 & 0 & 0 & 0 \\\ 0 & 0 & 0 & 0 \end{bmatrix} $





Class 8

The Unifying Theorem (Version 1)

1 and 2, 2 and 3 are equivalent but not 1 and 2