Cramer's Rule and Determinants

Front

What is Cramer's Rule?

Back

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

Front

What is a determinant?

Back

A determinant is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the matrix.

Front

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

Back

Front

How do you calculate the determinant of a 3x3 matrix?

Back

Front

What is the condition for a system of equations to have a unique solution using Cramer's Rule?

Back

The system must have a non-zero determinant for the coefficient matrix.

Front

What does it mean if the determinant of a matrix is zero?

Back

If the determinant is zero, the matrix is singular, meaning the system of equations may have no solutions or infinitely many solutions.

Front

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

Back

1. Write the system in matrix form. 2. Calculate the determinant of the coefficient matrix. 3. Replace one column of the coefficient matrix with the constant terms and calculate the determinant for each variable.

Front

What is the formula for finding a variable using Cramer's Rule?

Back

Front

Solve for x using Cramer's Rule: 2x + 3y = 6, x - y = 1.

Back

x = 3.

Front

Solve for y using Cramer's Rule: 2x + 3y = 6, x - y = 1.

Back

y = 0.