Ex. 9.Solve to find value of x.(Determinants)​

3

Question: Solve to find the value of x.

|111|

|3x3 |= 0

|1x2 |

Operations: R1 → R1 - R2 then R3 → R3 - R2 :-

Determinant is now :

| 0 1 0 |

| 3-x x 3-x |

| 1-x x 2-x |

Determinant of this is:

=> 0 - 1[(2-x)(3-x) - (3-x)(1-x)] + 0

=> - 1[6 - 2x - 3x + x² - (-3x + 3 - x + x²)]

=> - 1[6 - 5x + x² + 3x - 3 + x - x²]

=> - 1[ 3 - x]

Since determinant is 0 {as given}

=> -1(3 - x) = 0

=> 3 - x = 0

=> x = 3