Matrices & Determinants
Determinants
Grade Class 12
Question:
For a determinant Δ of order 3, the element a<sub>ij</sub> is defined as a<sub>ij</sub> = tan<sup>-1</sup>(tan(i - j)) ∀ i, j, then the value of Δ is equal to (where 'i' represents row and 'j' represents column)
Step-by-Step Solution
Key Concept: The determinant of a matrix where a_ij = f(i-j) and f is an odd function is zero for odd order matrices.
The matrix A = [a_ij] where a_ij = tan⁻^1(tan(i-j)). Since tan⁻^1(tan(x)) is an odd function, a_ij = -a_ji. Thus, A is a skew-symmetric matrix. The determinant of a skew-symmetric matrix of odd order is always 0.
Correct Answer: 0