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For the set of equations x1 + 2x2 + x3­ + 4x4 = 2 3x1 + 6x2 + 3x3 + 12x4 = 6 Which of the following statement is true?

For the set of equations x1 + 2x2 + x3­ + 4x4 = 2 3x1 + 6x2 + 3x3 + 12x4 = 6 Which of the following statement is true? Correct Answer Multiple non-trivial solutions exists

Given, system of equation

x1 + 2x2 + x3 + 4x4 = 2

3x1 + 6x2 + 3x3 + 12x4 = 6

Which is the non-homogeneous system of equations .

The augmented matrix is

Applying R2 → R2 – 3R1

Here, Rank of = 1 & Rank of A = 1

i.e. Rank of = Rank of A

So, the given system of equation is consistent. But the rank of A is less than the number of unknowns. So, the system of non-homogeneous equation will have infinitely many solutions. SO multiple, non-trivial solution exist.

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