Cramer's Rule Flashcard

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What is Cramer's Rule?

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Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns, using determinants.

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What is a determinant in the context of matrices?

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A determinant is a scalar value that is a function of the entries of a square matrix and provides important properties of the matrix, such as whether it is invertible.

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How do you calculate the determinant of a 2x2 matrix?

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What is the formula for the determinant of a 3x3 matrix?

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What is the significance of the determinant being zero?

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If the determinant of a matrix is zero, it indicates that the matrix is singular, meaning it does not have an inverse and the system of equations may have no solution or infinitely many solutions.

Front

How do you set up a system of equations for Cramer's Rule?

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Front

What is the x-coordinate solution using Cramer's Rule?

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What is the y-coordinate solution using Cramer's Rule?

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What is the z-coordinate solution using Cramer's Rule?

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How do you find the numerator for the x-coordinate in Cramer's Rule?

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The numerator for the x-coordinate is the determinant of the matrix formed by replacing the first column of the coefficient matrix with the constants from the equations.