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

glasskerfu

glasskerfu

Answered question

2021-11-07

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

Answer & Explanation

Theodore Schwartz

Theodore Schwartz

Skilled2021-11-08Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?