Determine if the system has a nontrivial solution. Try to use as few row operati

glasskerfu 2021-11-07 Answered
Determine if the system has a nontrivial solution. Try to use as few row operations as possible.
2x15x2+8x3=0
2x17x2+x3=0
4x1+2x2+7x3=0
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Expert Answer

Theodore Schwartz
Answered 2021-11-08 Author has 99 answers

Step 1
The given system is
2x15x2+8x3=0
2x17x2+x3=0
4x1+2x2+7x3=0
The augmented matrix is
[258027104270]
[258027104270]R1R3R2+1/2R1R2R31/2R1R3[42700692006920]
[42700692006920]R3R2R31/6R2R2~[4270013400000]
[4270013400000]R12R2R11/4R1R1 ~ [101780013400000]
Thus we get
x1+178x3=0x1=178x3
x234x3=0x2=34x3
Hence, the given system has a nontrivial solution because variable x3 is a free.
Result
The system has a nontrivial solution because variable x3 is a free

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