Chapter 8, Problem 126RE

To determine

Whether the given matrix are right or wrong.

Explanation of Solution

Given:

The matrix are given as:

  

Referring to the first matrix, it has unique solution which is obtained by the help of the back-substitution as:

  $x=1\text{and }y=1$

Now, the second matrix has the unique solution which is obtained by the matrix as:

  $x=1\text{and }y=1$

And the third matrix has the infinitely many solution and it is represented as:

  $x=3-2k\text{and}y=k\text{for some constant }k$

Since, the first two matrices are giving the same result and the third one produces the different result.

Therefore, all of three cannot be right.