Cramer's Rule Formula for Linear Equation

By using the Cramer's Rule we can solve the Algebraic linear equation. This is one of the real time application of Matrix. This worksheet may help you to know about the Cramer's Rule. Cramer's Rule which gives as expression for the solution of a system of linear equations with as many equations as unknown. If the determinant of the equation is not equal to zero means then Cramer's Rule can be applied otherwise Cramer's Rule can't be used. Cramer's Rule can valid where there is a unique solution. In other words, Cramer's Rule is used to find the solutions of a system of equations. This can be easily done by finding Matrix Determinant. If it is three linear equation and we need to find three unknown variable then by find 3x3 determinant. The following formula is used to find the solutions of a system of equation,
The solutions of the system of equations
a1x + b1x + c1x = d1
a2x + b2x + c2x = d2
a3x + b3x + c3x = d3
then,
X = Δx / Δ
Y = Δy / Δ
Z = Δz / Δ
Where,

Δ =
a1b1c1
a2b2c2
a3b3c3

Δx=
d1b1c1
d2b2c2
d3b3c3

Δy=
a1d1c1
a2d2c2
a3d3c3

Δz=
a1b1d1
a2b2d2
a3b3d3

The above worksheet is a walk through to understand the concept of how to apply Cramer's in Linear equation to find unknown values. When it comes to online calculation this Cramer's Rule Calculator is an essential tool to make the calculation easy.


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