If A^2 + B^2 + C^2 = 0 , then what is the value of vmatrix 1 & C & B C & 1 & A B & A & 1 vmatrix ?

Step-by-step solution

Given A^2 + B^2 + C^2 = 0 . Since the square of any real number is non-negative, the sum of squares can be zero if and only if each number is zero. Thus, A = 0 , B = 0 , and C = 0 . Substituting these values into the determinant, we get A = 0 = 1 , B = 0 = 1 , and C = 0 = 1 . The given determinant becomes: vmatrix 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 vmatrix Since all rows are identical, the value of the determinant is 0 . Answer: 0