Question

Find all values of and such that the system is 1. inconsistent; 2. consistent with exactly one solution; 3. consistent with infinitely many solutions. -ax1 - x2 = 3 1-2x1 + 4x2 = 6b.

Answer 1

Answer:

If -4a -2 = 0. a = -1/2 and b other than -11/6 the system is inconsistent.

If -4a -2 = 0. a = -1/2 and b = -11/6 the system is consistent with infinite solutions.

If  a is other than -1/2 the system is consistent with only one solution

Step-by-step explanation:

An inconsistent system is one that has no solutions.

An consistent system is one that has at least one solution.

Det (system) = (-4a - 2) ; Det (X1) = (13 -6b) ; Det (X2) = (a -6ab + 6)

If -4a -2 = 0. a = -1/2 and b other than -11/6 the system is inconsistent.

If -4a -2 = 0. a = -1/2 and b = -11/6 the system is consistent with infinite solutions.

If  a is other than -1/2 the system is consistent with only one solution