Find a maximal linearly independent subset of each of the following sets of vectors in .
-
.
-
.
-
.
- This set is a dependent set since
; hence, we cannot find a subset of size 4. Then, consider the three element subset
. This set is independent since
The third equation gives us
; hence, by the first equation
. Therefore,
and the set is independent.
- The set
is independent since the equation
gives us the equations
The only solution to this system is
; hence, this is a linearly independent subset.
- The set
is linearly independent since
gives us the system of equations
Thus, this set is linearly independent.