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Question
Examine the consistency of the system of equations5x−y+4z=5,2x+3y+5z=2,5x−2y+6z=−1
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Solution
Given system of equations5x−y+4z=5
2x+3y+5z=2
5x−2y+6z=−1
This can be written as AX=Bwhere A=⎡⎢⎣5−142355−26⎤⎥⎦,X=⎡⎢⎣xyz⎤⎥⎦,B=⎡⎢⎣52−1⎤⎥⎦
Here, |A|=5(18+10)+1(12−25)+4(−4−15)⇒|A|=140−13−76=51Since, |A|≠0Hence, the system of equations is consistent.
Given system of equations
5x−y+4z=52x+3y+5z=2
5x−2y+6z=−1
This can be written as
AX=B
where A=⎡⎢⎣5−142355−26⎤⎥⎦,X=⎡⎢⎣xyz⎤⎥⎦,B=⎡⎢⎣52−1⎤⎥⎦
Here, |A|=5(18+10)+1(12−25)+4(−4−15)
⇒|A|=140−13−76=51
Since, |A|≠0
Hence, the system of equations is consistent.
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