Problem 1

Determine if is a linear combination of , , and .

(a). , , , and

No is not a linear combination of of , , and .

Problem 2

Let , , and . For what value(s) of is in the plane generated by and .

Problem 3

Let , and and let be the set of all linear combinations of the columns of .

(a). Is in

Yes is in as the system above is consistent meaning there is some combination of the columns of which equals .

(b). Show that the Third Column of is in

The third column of must be in as we would just set the coefficients of the first two columns to zero and the third column to be 1 recovering the third column of .