<p>Can somebody help me with solving this question : Determine if the system has

Question

<p>Can somebody help me with solving this question : Determine if the system has a nontrivial solution. Try to use as few row operations as possible.</p>
<p><br /><img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-20119153454634516526943477276706.gif" alt="" align="absmiddle" /></p>
<p><img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-20119153626345165276236727033129.gif" alt="" align="absmiddle" /></p>

Explanation / Answer

-3x1 + 4x2 - 8x3 = 0 - (1)

-2x1 + 5x2 + 4x3 = 0 - (2)

use (2) + (-2/3)(1)

-3x1 + 4x2 - 8x3 = 0 - (1)

0x1 + (7/3)x2 + (28/3)x3 = 0 - (2)

Since it is reduced to the row-echelon form, and there is 2 pivot columun and a non-pivot columun.

The system is a non-trivial solution with infinity many solution.

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