Alg 2 ec 4.5 Flashcard (24/25)

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

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To use Cramer's Rule, express the system of equations in the form Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix.

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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, providing important properties about 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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How do you calculate the determinant of a 3x3 matrix?

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What does it mean if the determinant of a matrix is 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.

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How do you find the solution using Cramer's Rule?

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To find the solution using Cramer's Rule, calculate the determinants of the coefficient matrix and the matrices formed by replacing one column of the coefficient matrix with the constant matrix, then divide these determinants.

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The solution is (8, -3, 2).

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How do you solve for two variables using Cramer's Rule?

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For two variables, set up the equations in the form Ax = b, calculate the determinant of A, and then find the determinants for each variable by replacing the respective columns with the constant matrix.

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The solution is (4, 3).