Use Gaussian elimination method to find the solution of this equations. Thanks?!

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1 Answer
Feb 10, 2018

No solution exists.

Explanation:

Write the equation #x+4y+6z=-32# as the first line in an augmented matrix :

#[ (1,4,6,|,32) ]#

Write the equation #4x-y+3z=12# as the second line in the augmented matrix:

#[ (1,4,6,|,32), (4,-1,3,|,12) ]#

Write the equation, #5x+3y+9z = 20# as the third line in the augmented matrix:

#[ (1,4,6,|,32), (4,-1,3,|,12), (5,3,9,|,20) ]#

I shall use the notation in the Elementary Row Operations section of the reference to state what I am doing.

#-4R_1 + R_2 to R_2#

#[ (1,4,6,|,32), (0,-17,-21,|,-116), (5,3,9,|,20) ]#

#-5R_1 + R_3 to R_3#

#[ (1,4,6,|,32), (0,-17,-21,|,-116), (0,-17,-21,|,-140) ]#

Please observe that we have two identical rows equal to two different constants; this indicates that there is no solution.

As a double check, I entered the 3 equations into WolframAlpha and it confirmed my answer.