Consider each of the following systems in unknowns x, y, z: x + 2y + 2z...

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Consider each of the following systems in unknowns x, y, z: x + 2y + 2z = 1 x + ay+ 3z=3 x + 1ly+az = b (a) x-2y Xx- = 1 y + az = 2 ay +9z = b (b) (c) x + y + az = 1 x+ay+ z = 4 ax + y + z = b For which values of a does the system have a unique solution, and for which pairs of values (a, b) does the system have more than one solution? The value of b does not have any effect on whether the system has a unique solution. Why? Consider each of the following systems in unknowns x, y, z: x + 2y + 2z = 1 x + ay+ 3z=3 x + 1ly+az = b (a) x-2y Xx- = 1 y + az = 2 ay +9z = b (b) (c) x + y + az = 1 x+ay+ z = 4 ax + y + z = b For which values of a does the system have a unique solution, and for which pairs of values (a, b) does the system have more than one solution? The value of b does not have any effect on whether the system has a unique solution. Why? Consider each of the following systems in unknowns x, y, z: x + 2y + 2z = 1 x + ay+ 3z=3 x + 1ly+az = b (a) x-2y Xx- = 1 y + az = 2 ay +9z = b (b) (c) x + y + az = 1 x+ay+ z = 4 ax + y + z = b For which values of a does the system have a unique solution, and for which pairs of values (a, b) does the system have more than one solution? The value of b does not have any effect on whether the system has a unique solution. Why? Consider each of the following systems in unknowns x, y, z: x + 2y + 2z = 1 x + ay+ 3z=3 x + 1ly+az = b (a) x-2y Xx- = 1 y + az = 2 ay +9z = b (b) (c) x + y + az = 1 x+ay+ z = 4 ax + y + z = b For which values of a does the system have a unique solution, and for which pairs of values (a, b) does the system have more than one solution? The value of b does not have any effect on whether the system has a unique solution. Why?

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Solution a The system has a unique solution for all values of a To see why we can solve the first eq... View the full answer