TG EAMCET 2 May 2025 Shift 1 Paper

Given equations are x+y−z=1,
2x+4y−z=0‌ and ‌3x+4y+5z=18
The augmented matrix for the system is
A=[

1	1	−1	1
2	4	−1	0
3	4	5	18

]
We need to transform this matrix into
B=[

1	a	0	−1
0	2	1	b
0	0	c	32

]
Now, perform the row operation for matrix A, we get
R2⟶R2−2R1‌ and ‌R3⟶R3−3R1
A=[

1	1	−1	1
0	2	1	−2
0	1	8	15

]
Now, R3⟶R3−‌

1

2

R2
A=[

1	1	−1	1
0	2	1	−2
0	0	7.5	16

]
Apply R3⟶2R3, we get
A=[

1	1	−1	1
0	2	1	−2
0	0	15	32

]
Again apply R1⟶R1+R2, we get
A=[

1	3	0	−1
0	2	1	−2
0	0	15	32

]
Thus, a=3,b=−2 and c=15
⇒c=15
∴‌√a+b+c=√3+(−2)+15
‌=√1+15=√16=4