what is the cramer rule?
Solution
Cramer's Rule is a mathematical theorem that provides an explicit formula for the solution of a system of linear equations with as many equations as unknowns. It is named after Swiss mathematician Gabriel Cramer.
Here are the steps to apply Cramer's Rule:
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Write down the system of equations to be solved.
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Form the coefficient matrix of the system, and calculate its determinant.
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For each unknown in the system, form a new matrix by replacing the column in the coefficient matrix corresponding to that unknown with the column vector of constants on the right-hand side of the equations. Calculate the determinant of this new matrix.
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The value of each unknown is given by the ratio of the determinant of the matrix formed in step 3 to the determinant of the coefficient matrix from step 2.
Cramer's Rule can be applied to any number of equations, but it becomes increasingly complex as the number of equations (and therefore the size of the matrices) increases. It's also worth noting that Cramer's Rule can only be applied when the determinant of the coefficient matrix is not zero. If it is zero, the system of equations does not have a unique solution.
Similar Questions
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