Question

Find the dimensions of these 4 spaces. Which two of the spaces are the same? (a) column space of A, (b) column space of U, (c) row space of A, (d) row space of U:

A= [\begin{array}{ccc}1&1&0\\1&3&1\\3&1&-1\end{array}\right]
U= [\begin{array}{ccc}1&1&0\\0&2&1\\0&0&0\end{array}\right]

Answer 1

The dimensions of the column space and row space of matrices A and U are explained.

Step-by-step explanation:

The dimensions of the four spaces are:

(a) Column space of A: 3-dimensional

(b) Column space of U: 3-dimensional

(c) Row space of A: 2-dimensional

(d) Row space of U: 2-dimensional

The two spaces that are the same are the column space of A and the column space of U, both of which have dimensions of 3-dimensional.