Question
Asked Oct 20, 2019
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Use inverse matrices to find the solution of the system of equations.
2х
2z =
У
Зх
у +
Z=-9
13
х +у
Z =
(х, у, 2) 3
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Use inverse matrices to find the solution of the system of equations. 2х 2z = У Зх у + Z=-9 13 х +у Z = (х, у, 2) 3

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Expert Answer

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Step 1

The given system of equation can be written as,

АХ - В
Where,
-1 -2
8
х
A 3 -1
yand B -9
11
1
1
-1
13
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АХ - В Where, -1 -2 8 х A 3 -1 yand B -9 11 1 1 -1 13

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Step 2

Find the inverse matrix of matrix A.

Apply the elementary row operations to the augmented matrix [ A | I ], where I is the 3x3 identity matrix.

2 -1-2
10 0
AI3 - 1
10RR
0
-1
0
1
1
0
1
0 0
-1
1
RR-3R
3 -1 1
0
0
RR 2R
0 0
2
-1 -2
1
1
1
-1 0
0
3 R >
0
4
4
0
1
-2
0
-3
0
1
0
_
-1 0
1
0
1
RRR
-1
-1 0
4
3
0 1
4 RR3R
0 3 0 1
0
-2
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2 -1-2 10 0 AI3 - 1 10RR 0 -1 0 1 1 0 1 0 0 -1 1 RR-3R 3 -1 1 0 0 RR 2R 0 0 2 -1 -2 1 1 1 -1 0 0 3 R > 0 4 4 0 1 -2 0 -3 0 1 0 _ -1 0 1 0 1 RRR -1 -1 0 4 3 0 1 4 RR3R 0 3 0 1 0 -2

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Step 3

Continue to finding the...

1
10 00
4
4
1
AI0 1 1 0
R
4
-3
-3
0 0-31
4
1
1
1 0 0
0
4
-1
0 1-0
3
R RR
4
1
-1
0 0 1
4
12
1
0
4
1
1 0 0
4
-1
2
0 10
0
3
-1
0 0 1
1
-1
4
12
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1 10 00 4 4 1 AI0 1 1 0 R 4 -3 -3 0 0-31 4 1 1 1 0 0 0 4 -1 0 1-0 3 R RR 4 1 -1 0 0 1 4 12 1 0 4 1 1 0 0 4 -1 2 0 10 0 3 -1 0 0 1 1 -1 4 12

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