Question

For each part below, give an example of a linear system of three equations in three variables that has the given property. in each case, explain how you got your answer, possibly using sketches.

(a) has no solutions

(b) has exactly one solution which is (1, 2, 3).

(c) any point of the line given parametrically be (x, y, z) = (s − 2, 1 + 2s, s) is a solution and nothing else is.

(d) any point of the form (x, y, z) = (s1, s2, s1 − s2), with s1, s2 numbers, is a solution and nothing else is. Hint: The set of all such points is a plane in 3-space.

Answer 1