Consider a linear system whose augmented matrix is first row (1 1 2 | 0) second row (1 2 -3 | -1) third row (9 19 k |-9) For what value of k will the system have no solutions ?
System has no solutions for
If we write the system in matrix form we get:
The system has no solution if the determinant of the matrix is zero, so we look for such
The value of expression above is zero for
To calculate the determinant I used the Rule of Sarrus. It's described in Wikipedia under: https://en.wikipedia.org/wiki/Rule_of_Sarrus