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Sample edHelper.com - Matrices Worksheet

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Matrices
Use the inverse of the linear system to solve for x, y, and z.

1.   -9x - 3y - 2z = -72
-5x + 7y + 8z = 68
-1x - 4y + 6z = 37
A-1  =
 -37/393 -13/393 5/393 -11/393 28/393 -41/393 -9/262 11/262 13/131

2.   5x - 3y - 7z = -50
-1x + 4y - 6z = -40
8x - 9y + 2z = -2
A-1  =
 -2/3 1 2/3 -2/3 22/23 37/69 -1/3 7/23 17/69

3.   -9x - 7y + 1z = 15
-4x + 3y - 6z = 45
-8x + 5y - 2z = 39
A-1  =
 -2/41 3/164 -13/164 -10/123 -13/246 29/246 -1/123 -101/492 55/492

4.   -7x + 5y + 8z = 43
-6x - 3y + 4z = 16
-2x - 1y - 9z = 88
A-1  =
 -1/17 -37/527 -44/527 2/17 -79/527 20/527 0 1/31 -3/31

5.   -5x + 8y - 4z = -120
7x - 6y - 9z = -3
-2x - 1y + 3z = 11
A-1  =
 -27/187 -20/187 -96/187 -3/187 -23/187 -73/187 -19/187 -21/187 -26/187

6.   -3x - 7y - 2z = -24
1x - 4y - 9z = -117
6x - 8y - 5z = -165
A-1  =
 -52/467 -19/467 55/467 -49/467 27/467 -29/467 16/467 -66/467 19/467

7.   -4x + 6y + 3z = -36
1x - 9y - 7z = 39
-5x - 8y - 2z = -26
A-1  =
 -38/215 -12/215 -3/43 37/215 23/215 -5/43 -53/215 -62/215 6/43

8.   -6x - 8y - 5z = 54
3x + 7y - 2z = -39
-1x - 9y + 4z = 53
A-1  =
 1/12 77/120 17/40 -1/12 -29/120 -9/40 -1/6 -23/60 -3/20

9.   8x - 5y - 3z = 113
-6x + 1y - 4z = -39
2x - 9y + 7z = 5
A-1  =
 29/558 -1/9 -23/558 -17/279 -1/9 -25/279 -26/279 -1/9 11/279

10.   -5x + 7y - 3z = -95
-2x + 1y + 9z = -47
6x + 4y - 8z = 0
A-1  =
 -1/12 1/12 1/8 19/264 29/264 17/176 -7/264 31/264 3/176

11.   -9x - 3y - 4z = 91
-6x + 7y - 5z = 18
2x + 8y - 1z = -55
A-1  =
 -33 35 -43 16 -17 21 62 -66 81

12.   7x + 2y + 9z = -149
-3x - 1y + 5z = 12
6x - 8y - 4z = 30
A-1  =
 22/307 -32/307 19/614 9/307 -41/307 -31/307 15/307 34/307 -1/614

Sample
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