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Name _____________________________
Date ___________________

Matrices
(Answer ID # 0701653)
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  

 

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