The sum of the values of x so that the matrix ( array lll 2 & 2 & 1 1 & 3 & 1 1 & 2 & 2 array )-x ( array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ) is singular, is

Step-by-step solution

Let a matrix = [ array lll 2 & 2 & 1 1 & 3 & 1 1 & 2 & 2 array ]-x [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]= [ array ccc 2-x & 2 & 1 1 & 3-x & 1 1 & 2 & 2-x array ] Matrix A is a singular. |A|=0 | array ccc 2-x & 2 & 1 1 & 3-x & 1 1 & 2 & 2-x array |=0 On applying C₁ C₁+C₂+C₃ , we get aligned & | array ccc 5-x & 2 & 1 5-x & 3-x & 1 5-x & 2 & 2-x array |=0 & (5-x) | array ccc 1 & 2 & 1 1 & 3-x & 1 1 & 2 & 2-x array |=0 aligned On applying R₂ R₂-1 and R₃ R₃-R₁ , we get aligned (5-x) | array ccc 1 & 2 & 1 0 &