Consider the following system of equations: 2x1 − 4x2 + 3x3 − x4 + 2x5 = 03x1 − 6x2 + 5x3 − 2x4 + 4x5 = 05x1 − 10x2 + 7x3 − 3x4 + 18x5 = 0.find the general solution of the system.

The system has a corresponding augmented matrix

Let's get this into reduced row echelon form.

Add 3(row 1) to -2(row 2), and add 5(row 1) to -2(row 3):

Multiply through row 2 by -1:

Add -1(row 2) to row 3:

Multiply through row 3 by 1/2:

Add row 3 to row 2:

Add -3(row 2) and row 3 to row 1:

Multiply through row 1 by 1/2:

This tells us

The matrix has rank 3, so we can pick 2 free variables, say and . Then the general solution to the system is

where .

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step-by-step explanation: