Evaluate :
`| [ 0 , a , -b ] , [ -a , 0 , -c ] , [ b , c , 0 ] |`

If [ [ 1 , 0 , 0 ] , [ 0 ,1 , 0 ] , [ 0 , 0 , 1 ] ] [ [ a ] , [ b ] , [ c ] ] = [ [ 2 ] , [ 1 ] , [ -3 ] ] , then find the value of a + b + c

Evaluate |[0,c,b] , [c,0,a] , [b,a,0]| hence show that |[0,c,b] , [c,0,a] , [b,a,0]|^2= |[b^2+c^2,ab,ac] , [ab,c^2+a^2,bc] , [ca,bc,a^2+b^2]|=4a^2b^2c^2

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 andb(a+c)> a c

Let X = A . bar (BC) . Evaluate X for (a) A = 1 , B = 0 , C = 1 , (b) A = B = C = 1 and ( c) A = B = C = 0.

Find the value of ( a - b ) times ( a + b ) + ( b -c ) times ( b + c ) + ( c + a ) times ( c - a ) = A) -1 B) 0 C) 1

If a + b + c = 0 , then find the value of ( ( a + b ) / c + ( b + c )/a + ( c + a ) / b ) times ( a /( b + c ) + b /( c + a ) + c /( a + b ) ) is :

The roots of the equation ax^2+bx + c = 0 will be imaginary if, A) a gt 0 b=0 c lt 0 B) a gt 0 b =0 c gt 0 (C) a=0 b gt 0 c gt 0 (D) a gt 0, b gt 0 c =0

If a+b+c=0, solve the equation: |[a-x, c, b],[c,b-x, a],[b, a, c-x]|=0

Find the value of ( 5^0 + 6^0 + 7^0 ) ÷ ( a^0 + b^0 + c^0 )