Determine if the system Ax B where x and b have the appropr

Determine if the system Ax = B (where x and b have the appropriate number of components) has a solution for all choices of b.

A = -9 21

6 -14

Solution

The system of equations is Ax =B

and b has all components

Hence we can take as B not equal to 0

The system will have solution for A non singular

Det A = |A| = -9(-14)-21(6) = 126-126 =0

Since determinant A is zero, the system does not have unique solution for B not equal to 0.

If B =0 then we can have infinite dependent solutions for x and y.