Answer to Question #293753 in Linear Algebra for Hossain

Question

Consider the following system of equations:

1)

x + 3y + 5z = b1

2x + 4y + 6z = b2.

Show that there are no solutions if b2 = 2b1 and infinitely many solutions otherwise.

2)

x + 4y = b1

2x + 5y = b2

3x + 6y = b3.

Show that there is exactly one solution if b3 = 7b1 − 2b2 and no solutions otherwise.