Final answer:
To find the values of a for which the linear system has no solutions, use the concept of determinant. The system has no solutions when a = -5/2.
Step-by-step explanation:
To find the values of a for which the linear system has no solutions, we can use the concept of determinant. If the determinant of the coefficient matrix is 0, then the system has no solutions.
First, we write the augmented matrix for the system:
[1 -1 a | -2]
[-1 2 -a | 3]
[a 1 1 | 2]
Next, we calculate the determinant of the coefficient matrix:
det([[1 -1 a], [-1 2 -a], [a 1 1]])
Simplifying and expanding the determinant, we have:
2a + 5
Setting the determinant equal to 0 and solving for a:
2a + 5 = 0
2a = -5
a = -5/2
Therefore, the system has no solutions when a = -5/2.