Understanding Matrices

Solve the following system of equations using matrices: 2x + 3y = 8, 4x - y = 3

• x = 1, y = 4

• x = 3, y = 2

• x = -1, y = 0

• x = 2, y = 1

Find the determinant of the matrix: | 5 2 | | 3 1 |

• -1

• 2

• 0

• 8

Determine if the matrix is singular or non-singular: | 2 1 | | 4 2 |

• The determinant of the matrix is (2*2) - (1*4) = 0. Therefore, the matrix is singular.

• The determinant is 1

• The matrix is non-singular

• The matrix is symmetric

Solve the system of equations using matrices: x + y = 5, 2x - y = 3

• x = 4, y = 1

• x = 3, y = 2

• x = 1, y = 4

• x = 2, y = 3

Calculate the inverse of the matrix: | 3 1 | | 2 1 |

• [[1, -1], [-2, 3]]

• [[1, 1], [-2, 3]]

• [[1, -1], [2, 3]]

• [[3, 1], [2, 1]]

Find the product of the matrices: | 1 2 | | 3 4 | and | 5 6 | | 7 8 |

• | 19 22 | | 41 46 |

• | 2 4 | | 6 8 |

• | 10 12 | | 21 24 |

• | 15 18 | | 35 40 |

Solve the system of equations using matrices: 3x - 2y = 8, 2x + y = 4

• x = 4, y = 0

• x = 2, y = 1

• x = 5, y = -1

• x = 3, y = 2

Determine if the matrix is symmetric or not: | 1 2 | | 2 3 |

• Skew-symmetric

• Not symmetric

• Symmetric

• Diagonal

Find the eigenvalues of the matrix: | 4 1 | | 2 3 |

• λ = 6, 4

• λ = 0, 2

• λ = 3, 1

• λ = 5, 2

Solve the system of equations using matrices: 2x + y = 7, x - 3y = -5

• x = -3, y = 2

• x = 2, y = 5

• x = 4, y = 3

• x = 6, y = 1