Prove that `[ -> a , -> b , -> c+ -> d]=[ -> a , -> b , -> c]+[ -> a , -> b , -> d]`

Prove that [a xx b,a xx c,d]=(a*d)[a,b,c]

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , prove that: a : b = c : d .

If (a + b + c + d) : (a + b - c - d) = (a - b + c - d):(a-b-c+d) , then prove that a : b = c :d .

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , then prove that a : b = c : d

If A B C D is a parallelogram, then prove that a r\ (\ A B D)=\ a r\ (\ B C D)=\ a r\ (\ A B C)=\ a r\ (\ A C D)=1/2\ a r\ (|""|^(gm)A B C D)

If A B C D is a parallelogram, the prove that a r( A B D)=a r( B C D)=a r( A B C)=a r( A C D) =1/2a r (||^(gm) A B C D)

If A=[[a, b],[ c ,d]] , then a d j\ A is [[-d,-b],[-c, a]] (b) [[d,-b],[-c ,a]] (c) [[d, b],[ c, a]] (d) [[d, c],[ b ,a]]

If A=[[a, b],[ c ,d]] , then a d j\ A is (a) [[-d,-b],[-c, a]] (b) [[d,-b],[-c ,a]] (c) [[d, b],[ c, a]] (d) [[d, c],[ b ,a]]

Prove that :{{a},{a,b}}={{c},{c.d}}, iff a=c and b=d

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C . GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r(triangle A B D)=a r(triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A M_|_B D and C N _|_ B D . TO PROVE : A O=O C .