Exercise 3.3.3

See Example 3 in this section.

1.

The solution set is $(5,0)+\mathrm{span}(\{(-3,1)\})$.

2.

The solution set is $(\frac{2}{3},\frac{1}{3},0)+\mathrm{span}(\{(\frac{1}{3},\frac{2}{3},1)\})$.

3.

The solution set is $(3,0,0)+\mathrm{span}(\{(-1,1,1)\})$.

4.

The solution set is $(2,1,0)+\mathrm{span}(\{(0,1,1)\})$.

5.

The solution set is $(1,0,0,0)+\mathrm{span}(\{(-2,1,0,0),(3,0,1,0),(-1,0,0,1)\})$.

6.

The solution set is $(1,2)+\mathrm{span}(\{(0,0)\})$.

7.

The solution set is $(-1,1,0,0)+\mathrm{span}(\{(-3,1,1,0),(1,-1,0,1)\})$.