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If a, b and c are three coplanar vectors. If a is not parallel to b, show that c=(|[c*a, a*b], [c*b, b*b]|a+|[a*a, c*a], [a*b, c*b]|b)/(|[a*a, a*b], [a*b, b*b]|) .
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
If A B=A and B A=B , then show that A^2=A , B^2=B .
If A B=A and B A=B , then show that A^2=A , B^2=B .
For all set A and B, (A uu B) - B = A - B .
Matrices A and B will be inverse of each other only if (A) A B=B A (B) A B=B A=0 (C) A B=0,B A=I (D) A B=B A=I
Give examples of matrices A and B such that A B!=B A . (ii) A and B such that A B=O but A!=O ,\ B!=O
Give examples of matrices A and B such that A B=O but B A!=O . (ii) A ,\ B and C such that A B=A C but B!=C ,\ A!=O .
Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ \ A B=O and B A!=O (ii) A!=O ,\ \ B!=O ,\ \ A B=B A=O .
Find the sum of the series upto n terms 0.b+0.b b+0.b b b +0.b b b b+"......",AA " b" in N " and "1 le b le 9.
JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAINS-QUESTION