- #1

- 551

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Find the solutions of the following system of linear equations:

x + 3y - z = 1

2x + y + 2z = 3

5x + z = 2

I put these into the form Ax = b, where

A = (1 3 -1)

(2 1 2 )

(5 0 1 )

x = (x)

(y)

(z)

b = (1)

(3)

(2)

I worked out det A = 20.

Cramer's rule says the solutions are given by:

x = (1/det A) | 1 3 -1 | => x = 1/10

| 3 1 2 |

| 2 0 1 |

y = (1/det A) | 1 1 -1 | => y = 9/10

| 2 3 2 |

| 5 2 1 |

z = (1/det A) | 1 3 1 | => z = 11/10

| 2 1 3 |

| 5 0 2 |

These solutions are wrong, where have I gone wrong?? Grr.

When I work out the answers algebraically, I get x = 1/5, y = 3/5 and z = 1. These are correct.