AP EAMCET2012MathematicsMatrices
Let A= [ array rrr -1 & -2 & -3 3 & 4 & 5 4 & 5 & 6 array ], B= [ array cr 1 & -2 -1 & 2 array ] and C= [ array lll 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 array ] , if a, b and c respectively, denote the ranks of A, B and C , then the correct order of these number is
Options
- Aa < b < c
- Bc < b < a
- Cb < a < c
- Da < c < b
Correct answer
C. b < a < c
Step-by-step solution
Given, A= [ array rrr -1 & -2 & -3 3 & 4 & 5 4 & 5 & 6 array ] aligned |A| & =-1(24-25)+2(18-20)-3(15-16) & =1-4+3=0 aligned Now, | array ll 4 & 5 5 & 6 array |=24-25=-1 0 Rank of A=a=2B= [ array rr 1 & -2 -1 & 2 array ] |B|=2-2=0 Rank of B=b=1 and C= [ array ccc 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 array ]|C|=2(4-0)=8 0 Rank of C=3, c=3b < a < c ( 1 < 2 < 3)