Question

Please help me solve for what values of a and b the following system will have (a) a unique solution, (b) no solutions, and (c) infinite solutions.

Also, please explain how you got your answers. I know it has to do with the rank, but I'm not sure how to find it and how far to reduce the matrix.

x - 2y = 5

2x - y - 3az = 4

-x +bz = a

Answer 1

Sure, let's solve the given equations one by one.

1) x - 2y = 5

To solve for 'x' in terms of 'y', we can add '2y' to both sides of the equation:

x - 2y + 2y = 5 + 2y

Simplifying the equation:

x = 5 + 2y

Therefore, the solution of the equation is:

x = 5 + 2y

2) 2x - y - 3az = 4

To solve for 'y' in terms of 'x' and 'az', we can rearrange the given equation as:

y = 2x - 3az - 4

Therefore, the solution of the equation is:

y = 2x - 3az - 4

3) -x + bz = a

To solve for 'x' in terms of 'a' and 'b', we can rearrange the given equation as:

x = bz - a

Therefore, the solution of the equation is:

x = bz - a

I hope this helps!