Linear Algebra Exercise

Matrix Method: Problems

  1. 4x + 4y + 4z = 12

    x + 5y + 6z = -16

    3x + y + z = 17

  2. 4x + y + 4z = 36

    3x + 4y + z = 24

    1000x + 3y + 2z = 28

  3. 2x + 6y + z = 16

    -x – 4y + 6z = 18

    x + y + z = 10

  4. 3x + 4y – z = 1

    -2x + y + z = 3

    12x + 12y + 12z = 0

  5. 2x – y + z = 17

    1/2x + 2y – z = 10

    -x + 5y – z = 1

  6. 2x + 2y + 2z = 13

    4x + y – z = 0

    -2x + 4y – z = 3

  7. 5/2x + 1/3y – 3/2z = 0

    2x + 3y – z = 9

    -2x + y + 2z = 7

  8. 2x + y + z = 49

    3x – z = 0

    2x – y = 0

  9. 23x + y + z = 6

    46x + 2y – z = 3

    69x – y – 2z = -5

  10. 2x + y – z = 15

    -2x – y + z = -5

    7x + 2y + 2z = -4

  11. 2x + 3y – z = 25

    x + 4y + z = 25

    x – 6y + 5z = 25

  12. -2x + 2y + 2z = 120

    3x + 3/4y + 3/5z = 150

    1/3x + 1/4y + 1/5z = 30

  13. 2x + y – z = 12

    x + 2y – 2z = 6

    3x – y + 4z = 36


Answers

  1. x = 7, y = 1, z = -3
  2. x = 0, y = 4, z = 8
  3. x = 6, y = 0, z = 4
  4. x = -1, y = 1, z = 0
  5. x = 10, y = 2, z = -1
  6. x = 1/2, y = 2, z = 4
  7. x = 2, y = 3, z = 4
  8. x = 7, y = 14, z = 21
  9. x = 1/23, y = 2, z = 3
  10. x = 2, y = 1, z = -10
  11. x = 12, y = 2, z = 5
  12. x = 30, y = 40, z = 50
  13. x = 6, y = 6, z = 6

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