Question

1.34 Given a system of equations:
x + 2y + 2z = b
5x + y + 3z = b 2
Which of the following is true regarding its
solution?
(a) The system has a unique solution for any given
b, and be
(b) The system will have infinitely many solutions
for any given b, and be
(c) Whether or not a solution exists depends on
the given b, and bą
(d) The system would have no solution for any
values of b, and be
[2014: 1 Mark, Set-1)
in given as follows:​

Answer 1

Answer:

Option C is correct whether would have no solution for any values of b

Answer 2

The correct answer is option (b) The system will have infinitely many solutions for any given b₁ and b₂.

Explanation:

• The system Ax=B, with coefficient matrix A and augmented matrix AB the number of unknown is n.
• The various possibilities for solving the system are:
• Ax= B is inconsistent if and only if rank A < rank AB.
• Ax= B has unique solution if and only if rank A= rank AB = n.
• Ax= B is infinitely many solutions if and only if rank A > rank AB.
• Here, in the ques there exist two non-zero irrespective of values of b₁ and b₂.
• Therefore, have infinitely many solutions