Question

The value of the cofactor of the element of second row and third column in the matrix [4 3 2; 2 −1 0; 1 2 3] is :

If A = [aij] = [[2, -1, 5], [1, 3, 2], [5, 0, 4]] and cij is the cofactor of element aij, then the value of a21 · c11 + a22 · c12 + a23 · c13 is :

Obtain the value of Δ = |[1+x, 1, 1], [1, 1+y, 1], [1, 1, 1+z]| in terms of x, y and z. Further, if Δ = 0 and x, y, z are non-zero real numbers, prove that x⁻¹ + y⁻¹ + z⁻¹ = −1.

If Δ₁ = |1 0 0; 0 2 0; 0 0 3| and Δ₂ = |0 2 0; 1 0 0; 0 0 6|, then