Exercise 2.2.32

The question deals with 100 equations $\mathit{Ax}=0$ when $A$ is singular. (a) Some linear combination of the 100 rows is the row of 100 zeros.

(b) Some linear combination of the 100 columns is the column of zeros.

(c) A very singular matrix has all ones: $A=$ ones $(100)$. A better example has 99 random rows (or the numbers $1^i,\dots ,100^i$ in those rows). The 100 th row could be the sum of the first 99 rows (or any other combination of those rows with no zeros).

(d) The row picture has 100 planes meeting along a common line through 0 . The column picture has 100 vectors all in the same 99-dimensional hyperplane.