Find the inverse of the matrix
A= [a+ib−c+idc+ida−ib], if a2+b2+c2+d2=1
If =∣∣abcabcabcb2cc2aa2bc2bca2b2a∣∣=0,(a,b,c∈R) and are all different and nonzero), then prove that a+b+c=0.
Consider the system of the equation kx+y+z=1,x+ky+z=k,andx+y+kz=k2˙ Statement 1: System equations has infinite solutions when k=1. Statement 2: If the determinant ∣∣111kk1k21k∣∣=0, t hen k=−1.
The determinant ∣abaα+cbα+caα+α+c0∣=0, if a,b,c are in A.P. a,b,c are in G.P. a,b,c are in H.P. α is a root of the equation ax2+bc+c=0 (x−α) is a factor of ax2+2bx+c
Prove that the value of each the following determinants is zero: ∣∣a1a2a3la1+mb1la2+mb2la3+mb3b1b2b3∣∣