ISRO2012-ECE: Engineering Mathematics

Question

The system of equations $x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8$ has

1. A unique solution
2. No solution
3. An infinite number of solutions
4. None of these

Comments

Ax = b has a unique solution if and only if rank[A] = rank[A|b] = n where n is number of unknown variables 

Answer 1

Answer Unique Solution

Answer 2

x + y + z = 6, 2x+ y +z = 7, x + 2 y +z = 8

              

1	1	1	6
2	1	1	7
1	2	1	8

we can also find it using Rank 

Ax = b has a unique solution if and only if rank[A] = rank[A|b] = n where n is number of unknown variables 

rank[A] = rank[A|b] = 3 

hence unique solution

Answer 3

Option a