Let us use Gauss-Jordan method to solve the following system of linear equations:
⎩⎨⎧y−10z=−82x−6y=8x+2z=7.
⎝⎛0211−60−1002−887⎠⎞ ~ ⎝⎛10201−62−1007−88⎠⎞ ~ ∣∣−2R1+R3∣∣ ~
⎝⎛10001−62−10−47−8−6⎠⎞ ~ ∣∣6R2+R3∣∣ ~ ⎝⎛1000102−10−647−8−54⎠⎞ ~
∣∣−641R3∣∣ ~ ⎝⎛1000102−1017−827/32⎠⎞ ~ ∣∣R1−2R3,R2+10R3∣∣ ~
⎝⎛10001000185/167/1627/32⎠⎞.
It follows that x=1685, y=167, z=3227.
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