## Question

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

Determine if the system has a nontrivial solution. Try to use as few row operations as possible 4x1-6x2 + 13x3 = 0 -4x1-2x2-7x3 = 0 8x1 4x2+14x30 Choose the correct answer below. O A. O B. O C. The system has a nontrivial solution. It is impossible to determine. The system has only a trivial solution.

## Answers

system is

augmented matrix is

4 -6 13 -4 -2 -7 8 4 14 convert into Reduced Row Eschelon Form...

Divide row1 by 4

1 -3/2 13/4 -4 -2 -7 8 4 14

Add (4 * row1) to row2

1 -3/2 13/4 0 -8 6 8 4 14

Add (-8 * row1) to row3

1 -3/2 13/4 0 -8 6 0 16 -12

Divide row2 by -8

1 -3/2 13/4 0 1 -3/4 0 16 -12

Add (-16 * row2) to row3

1 -3/2 13/4 0 1 -3/4 0 0 0

Add (3/2 * row2) to row1

1 0 17/8 0 1 -3/4 0 0 0 reduced system is

.................free variable

non trivial solution is

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