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For parts a and b, find a basis for the solution set of the homogeneous linear...

For parts a and b, find a basis for the solution set of the homogeneous linear systems. Show all algebraic steps.

a. x1 + x2 + x3 = 0.

x1 - x2 - x3 = 0

b. x1 + 2x2 - 2x3 + x4 = 0.

x1 - 2x2 + 2x3 + x4 = 0.

for parts c and d use your solutions to parts a and b to find all solutions to the following linear systems. show all algebraic steps.

c. x1 + x2 + x3 = 3.

x1 - x2 - x3 = -1

d. x1 + 2x2 - 2x3 + x4 = -2.

x1 - 2x2 + 2x3 + x4 = 10.

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