Without expanding the determinants, prove that `|103 115 114 111 108 106 104 113 116|+|113 116 104 108 106 111 115 114 103|=0`

Without expanding the determinants, prove that |(103, 115, 114), (111, 108, 106), (104, 113, 116)|+|(113, 116, 104), (108, 106, 111), (115, 114, 103)|=0

Without expanding the determinants, prove that |(103, 115, 114), (111, 108, 106), (104, 113, 116)|+|(113, 116, 104), (108, 106, 111), (115, 114, 103)|=0

Without expanding the determinants Prove that |{:(103,,115,,114),(111,,108,,106),(104,,113,,116):}| + |{:(113,,116,,104),(108,,106,,111),(115,,114,,103):}|=0

Without expanding the determinants Prove that |{:(103,,115,,114),(111,,108,,106),(104,,113,,116):}| + |{:(113,,116,,104),(108,,106,,111),(115,,114,,103):}|=0

Without expanding the determinants Prove that |{:(103,,115,,114),(111,,108,,106),(104,,113,,116):}| + |{:(113,,116,,104),(108,,106,,111),(115,,114,,103):}|=0

Find the value of the determinant |101 102 103 104 105 106 107 108 109|

Without expanding prove that: |x+yy+zz+xzxy111|=0

97, 101, 103, 107, 111, 113

Find the value of the determinant |[101 ,102 ,103],[ 104 ,105 ,106],[ 107, 108, 109]|

Without expanding, prove that Delta=|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0