_{n}with the solution vector and take the determinant of that matrix. If you divide the determinant of the coefficient matrix with the solution vector over the determinant of the coefficient matrix we get the solution to x

_{n}given that the determinant of the coefficient matrix is nonzero.

Example-

|2 3 7 |

|4 5 13|

So to solve this we take the determinant of the coefficient matrix

|2 3|

|4 5|

det=(2)5-3(4)

det=10-12

det=-2

|7 3|

|13 5|

det=(7)5-3(13)

det=35-39

det=-4

|2 7 |

|4 13|

det=(2)13-4(7)

det=26-28

det=-2

x

_{1}= -2/-2 = 1

x

_{2}= -4/-2 = 2

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