4.2: Null Spaces, Column Spaces, and Linea...
20. A = [1 -3 2 0 -5]
21. With A as in Exercise 17, find a nonzero vector in Nul A, a nonzero
vector in Col A, and a nonzero vector in Row A.
22. With A as in Exercise 3, find a nonzero vector in Nul A, a nonzero
vector in Col A, and a nonzero vector in Row A.
23. \begin{equation*}
\text{Let } A = \begin{bmatrix} -6 & 12 \\ -3 & 6 \end{bmatrix} \text{ and } w = \begin{bmatrix} 2 \\ 1 \end{bmatrix}. \text{ Determine if } w \text{ is in Col A. Is } w \text{ in }\\ \text{Nul A?}
\end{equation*}
24. \begin{equation*}
\text{Let } A = \begin{bmatrix} -8 & -2 & -9 \\ 6 & 4 & 8 \\ 4 & 0 & 4 \end{bmatrix} \text{ and } w = \begin{bmatrix} 2 \\ 1 \\ -2 \end{bmatrix}. \text{ Determine if } w \text{ is in Col }\\ \text{A. Is } w \text{ in Nul A?}
\end{equation*}
In Exercises 25-38, A denotes an $m \times n$ matrix. Mark each statement True or
False (T/F). Justify each answer.
25. (T/F) The null space of A is the solution set of the equation $Ax = 0$.
