\[\left [\begin{array}{c|c} A & \vec {b}\\ \end{array}\right ]\]
corresponding to a system of linear equations.
True or False?
- (a)
- If there is more than one solution, \(\left [\begin{array}{c|c} A & \vec {b}\\ \end{array}\right ]\) has a row of zeros.
True False
- (b)
- If \(\left [\begin{array}{c|c} A & \vec {b}\\ \end{array}\right ]\) has a row of zeros, there is more than one solution.
True False
- (c)
- If there is no solution, \(\mbox {rref}(A)\) has a row of zeros.
True False
- (d)
- If \(\mbox {rref}(A)\) has a row of zeros, there is no solution.
True False
- (e)
- There is NO system that is inconsistent for every \(\vec {b}\).
True False
- (f)
- If the system is consistent for some choice of \(\vec {b}\), it is consistent for every choice of
\(\vec {b}\).
True False