AP EAPCET 24-Aug-2021 Shift 1 Paper

Option (a) Let A=[

10	11	12
11	12	13
12	13	14

]
Applying R1→R1−R2,R2→R2−R3
[

−1	−1	−1
−1	−1	−1
12	13	14

]
Applying R2→R2−R1,R3→R3+12R1,
[

−1	−1	−1
0	0	0
0	1	2

]
Applying R2↔R3
[

−1	−1	−1
0	1	2
0	0	0

] this is echelon form
∴ Rank of matrix A=2
Option(b) B=[

0	−51	101
51	0	−581
−101	581	0

]
∵ BT=−B,∴B is skew-symmetric matrix.
∵ Rank of skew-symmetric matrix is always an even number rank of B≠3
Option (c) C=[

0	1	2
−1	0	5
−2	7	0

]
Applying R2↔R1.
[

−1	0	5
0	1	2
−2	7	0

]
R1→R1−R3
⇒[

1	−7	5
0	1	2
−2	7	0

]
Applying R3→R3+2R1[

1	−7	5
0	1	2
0	−7	10

]
Applying R3→R3+7R2,R1→R1+7R2
[

1	0	19
0	1	2
0	0	24

]
Applying R3→

1

24

R3[

1	0	19
0	1	2
0	0	1

]
Applying R1→R1−19R3,R2→R2−2R3
[

1	0	0
0	1	0
0	0	1

]
∴ Rank of matrix C=3
Option (d) D=[

1	2	3
2	4	6
3	6	9

]
Applying R2→R2−2R1,R3→R3−3R1
[

1	2	3
0	0	0
0	0	0

]
∴ Rank of matrix D=1
Hence, option (c) is the correct answer.