Find the values of a,b and c if the matrix `A={:[(0,2b,c),(a,b,-c),(a,-b,c)]` satisfies A'A = I.

Find the value of a, b, c and d from the equation: [(a-b,2a+c),(2a-b,3c+d)]=[(-1,5),(0,13)]

If a,b,c, are non-zero real numbers, then the inverse of matrix A = [(a,0,0),(0,b,0),(0,0,c)] is -

Find the value of a if [a-b2a+c2a-b3c+d]=[-1 5 0 13]

If the determinant of the matrix [(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))] is denoted by D, then the determinant of the matrix [(a_(1)+3b_(1)-4c_(1),b_(1),4c_(1)),(a_(2)+3b_(2)-4c_(2),b_(2),4c_(2)),(a_(3)+3b_(3)-4c_(3),b_(3),4c_(3))] will be -

Prove that, |{:(-2a,a,a),(-2b,b,b),(c+a,b+c,-2c):}|=0

Using the property of determinants and without expanding {:|( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)|:} =0

Given a matrix A=[(a,b,c), (b,c,a), (c,a,b)],where a ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.

If a,b and c are real numbers, and Delta ={:|( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) |:}=0 Show that either a+b+c=0 "or" a= b= c .

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c