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Name _____________________________
Date ___________________

Matrices
(Answer ID # 0211938)
Complete.
1.  
  15    -6    17  
  13    16    -7  
  +  
  -15    -11    -4  
  -14    17    11  
2.  
  19  
  13  
  +  
  17  
  20  

Complete.
3.  
  15    -17    -6    1  
  -10    11    7    -2  
  -19    19    -15    4  
  -  
  -7    2    -1    3  
  -14    -17    5    14  
  17    -11    13    9  
4.  
  -7  
  -20  
  18  
  -  
  17  
  -11  
  6  

Complete.
5.  
  4  
  -3  
  +  
  -20  
  -18  
  -  
  18  
  9  

Complete.
6.  
  -18    17    2  
  0    -12    -9  
  -8    11    -15  
  8    10    6  
  -  
  4    12    18  
  -1    13    5  
  14    -4    -5  
  -2    -19    9  
  -  
  -7    -10    -13  
  11    -15    -2  
  -6    3    4  
  12    16    8  

 

Find the product. If the product is not defined, state the reason.
7.  
  11    -1    19    12  
  6    -2    2    3  
  10    9    0    -16  
  -6    18    13    -4  
  
  -17    0    -14    6  
  -2    19    10    -6  
  16    -7    14    8  
  15    -16    -13    -9  

Solve for x and y.
8.  
  x    8  
  16    -19  
  
  17    -15  
  14    -3  
  =  
  -228    276  
  y    -183  

Calculate the determinant of each matrix. Show your work.
9.  
  18    5  
  9    -4  
10.  
  -6    18  
  -17    16  
11.  
  -9    5  
  16    -16  

Calculate the determinant of each matrix. Show your work.
12.   Use the diagonals method.
  0    14    -6  
  1    -11    -13  
  -20    15    11  
13.   Expand along column 1.
  -8    17    -14  
  -17    -6    9  
  8    2    -9  
14.  
  11    -19  
  18    -11  

 

Use determinants to calculate the area. Show your work.
15.   Calculate the area of the triangle with the following points:
(0, -4), (2, -2), (-4, -2)
16.   Calculate the area of the triangle with the following points:
(-6, 1), (0, 0), (-2, 3)
17.   Calculate the area of the triangle with the following points:
(0, -5), (-1, -9), (5, -1)

Use determinants to calculate the area. Show your work.
18.   Calculate the area of the quadrilateral with the following points:
(-1, -3), (0, 0), (2, 1), (4, -7)
19.   Calculate the area of the quadrilateral with the following points:
(-1, 3), (-1, 8), (3, 5), (7, -1)
20.   Calculate the area of the quadrilateral with the following points:
(-4, -2), (-2, 1), (1, 0), (5, -3)

Complete.
21.   Find the inverse of:
  8    -3  
  -5    -8  
22.   Find the inverse of:
  7    -5  
  4    -10  
23.   Find the inverse of:
  6    -6  
  -4    12  

Solve the matrix equation.
24.  
  9    -10  
  12    0  
  X    =  
  62    59  
  -24    12  
25.  
  -6    -2  
  5    -8  
  X    =  
  -84    60  
  -17    -79  

 

Write the system of linear equations represented by each matrix equation.
26.  
  8    -4  
  3    2  
 
  x  
  y  
  =  
  148  
  24  
27.  
  -9    -6    5  
  -8    -9    -4  
  5    -1    -7  
 
  x  
  y  
  z  
  =  
  28  
  55  
  -3  

Use the inverse of the linear system to solve for x, y, and z.
28.   -3x + 8y + 1z = -18
-2x - 6y - 9z = -15
-6x + 5y + 3z = 13
A-1  =  
  27/353    -19/353    -66/353  
  60/353    -3/353    -29/353  
  -46/353    -33/353    34/353  
29.   9x - 8y + 4z = 52
-1x - 7y - 2z = 13
-2x + 8y + 4z = -52
A-1  =  
  3/65    -16/65    -11/65  
  -2/65    -11/65    -7/130  
  11/130    14/65    71/260  

Write the augmented matrix for the linear system and then solve.
30.   -6x - 7y = -12
3x + 2y = 15
31.   -1x + 3y = -14
5x - 6y = 25

Solve each system of equations using Cramer's rule.
32.   -6x - 4y + 7z = -132
1x - 6y + 3z = -13
-4x - 7y - 9z = 53
33.   5x - 2y = -7
-4x + 5y = -8
34.   -3x + 7y = 65
-9x + 6y = -15

 

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