Question

In: Math

Convert the system 3x1 +13x2 - 14x3 = -14 x1 + 4x2 -5x3 = -4 -7x1...

Convert the system

3x1 +13x2 - 14x3 = -14

x1 + 4x2 -5x3 = -4

-7x1 - 25x2 +39x3 = 20

to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions.

Augmented matrix:

Echelon form:

Is the system consistent?

Solution (x1,x2,x3) =

Solutions

Expert Solution

augmented matrix is

3	13	-14	-14
1	4	-5	-4
-7	-25	39	20

convert into Reduced Row Eschelon Form...

Divide row1 by 3

1	13/3	-14/3	-14/3
1	4	-5	-4
-7	-25	39	20

Add (-1 * row1) to row2

1	13/3	-14/3	-14/3
0	-1/3	-1/3	2/3
-7	-25	39	20

Add (7 * row1) to row3

1	13/3	-14/3	-14/3
0	-1/3	-1/3	2/3
0	16/3	19/3	-38/3

Divide row2 by -1/3

1	13/3	-14/3	-14/3
0	1	1	-2
0	16/3	19/3	-38/3

Add (-16/3 * row2) to row3

1	13/3	-14/3	-14/3
0	1	1	-2
0	0	1	-2

Add (-1 * row3) to row2

1	13/3	-14/3	-14/3
0	1	0	0
0	0	1	-2

Add (14/3 * row3) to row1

1	13/3	0	-14
0	1	0	0
0	0	1	-2

Add (-13/3 * row2) to row1

1	0	0	-14
0	1	0	0
0	0	1	-2

here for every column there is one pivot entry so system is consistent

so unique solution is

milcah answered 1 year ago

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