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Summary Solving systems of equations using Cramer's Rule $5.97   Add to cart
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Summary Solving systems of equations using Cramer's Rule
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Solving systems of equations using Cramer's Rule. The determinants of the coefficient and unknown matrices are found. Cramer's rule is applied to find the unknowns.

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  • November 23, 2023
  • 1
  • 2022/2023
  • Summary

Subjects

  • cramers rule linear algebra systems of equation

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  • Secondary school
  • Unknown
  • 2

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LinoGuer

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Solve the following system of equations using Cramer’s Rule


2x +6y −4z = 1
1x +3y −2z = 4
2x +1y −3z = −7



Explanation and answer.

Cramer’s Rule

For the given system. Let D the coefficient matrix. Let Dx the matrix obtained replacing
the x-coefficient by B-coefficient. Let Dy the matrix obtained replacing the y-coefficient by
B-coefficient. Let Dz the matrix obtained replacing the z-coefficient by B-coefficient.

When the determinant |D| =
6 0 the solutions are given by


|Dx | |Dy | |Dz |
x= ,y= ,z=
|D| |D| |D|

 
1
We have B =  4 
−7

Coefficient matrix
 
2 6 −4
D = 1 3 −2
2 1 −3

We calculate the determinants
2 6 −4
|D| = 1 3 −2 = −18 + (−24) + (−4) − (−24 + (−18) + (−4)) = 0
2 1 −3

The system has no solution. Division by 0 does not exist.




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