# Determinants Worksheets

Use our worksheets to find the determinants of order 2 x 2 or 3 x 3. Cramer uses determinant to identify the solutions of systems of equations in two and three variables. We have handful of worksheets in Cramer's rule and determinants.

## 2 x 2 Determinants

2 x 2 Determinants - Integers

Evaluate 2 x 2 determinants by cross multiplication. Entries are integers.

Simple Determinants-2

Simple Determinants-3

Simple Determinants-4

2 x 2 Determinants - Fractions

Find the value of the determinants. Entries are fractions.

Moderate Determinants-2

## 3 x 3 Determinants

3 x 3 Determinants

Evaluation of 3 x 3 determinants performed along any of the rows or columns.

Easy-2

Difficult

## Cramer's Rule: Identifying Number of Solutions

Identifying Number of Solutions Using Cramer's Rule

System of equations in two variables has unique, infinite or no solution. Determinants and Cramer's rule help us to identify the number of solutions. Unique: None of Del, Del x and Del y zero. Infinite: Del, Del x and Del y are zero. No solution: Del = 0; Either Del x or Del y non zero

Identify solutions-2

## Cramer's Rule: Solving Equations

Solve Using Cramer's Rule

If the value of determinant is non-zero, then the solution exists. Find del, del x and del y. x = del x / del; y = del y / del

Two Variables Easy-2

Find Solution Using Cramer's Rule

Couple of determinant worksheets based on solving equations in two variables with fraction coefficients but solutions in integers.

Two Variables Difficult-1

Two Variables Difficult-2

Equations in Three Variables Easy

Solve using Cramer's rule.

Three Variables Easy-2

Three Variables Easy-3

Equations in Three Variables Hard

Solve the system of equations in three variables using Cramer's rule. Coefficients are in fractions but answers in integers.

Three Variables Difficult-1

Three Variables Difficult-2

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