Math Problem Solver

Section 1: System of Linear Equations

Solve the following systems using the specified methods.

Question 1:

Solve the following system using the Substitution Method:

1. 2x + 3y = 8

2. 4x - y = 2

Question 2:

Solve the following system using the Elimination Method:

1. 5x - 2y = 7

2. 3x + 4y = 1

Question 3:

Solve the following system using Cramer’s Rule:

1. x + 2y = 5

2. 3x - y = 4

Question 4:

Solve the following system using the Matrix Method:

1. x + y + z = 6

2. 2x - y + 3z = 14

3. 3x + 4y - 2z = 10

Question 5:

Solve the following system using the Matrix Method:

1. 2x - y + z = 4

2. x + 3y - 2z = 5

3. 3x - 2y + 4z = 7

Section 2: Matrices

Solve the following matrix-related problems.

Question 6:

Find the adjoint of matrix A:

A = | 2 -1 3 |

| 1 0 4 |

| 3 2 -2 |

Question 7:

Find the determinant of matrix A:

A = | 4 3 -1 |

| 2 1 5 |

| 3 -2 6 |

Question 8:

Find the inverse of matrix A:

A = | 1 2 3 |

| 0 1 4 |

| 5 6 0 |

Question 9:

Find the determinant of the following matrix:

A = | 2 3 4 |

| 1 -2 3 |

| 0 5 -1 |

Question 10:

Find the determinant of the following matrix:

A = | 1 2 3 |

| 4 5 6 |

| 7 8 9 |