Advanced Math - Chapter 8: Matrices and Determinants

Determine the order of the matrix.
⌈ 3 -1 0 6 ⌉
⌊ -2 7 1 4 ⌋

• The order of the matrix is 2 x 4.

• The order of the matrix is 4 x 2.

• The order of the matrix is 2 x 3.

• The order of the matrix is 3 x 2.

Determine whether the matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form.
⌈ 1 0 2 1 ⌉
| 0 1 -3 10 |
⌊ 0 0 1 0 ⌋

• The matrix is in row-echelon form but not in reduced row-echelon form.

• The matrix is not in row-echelon form.

• The matrix is in reduced row-echelon form.

• The matrix is neither in row-echelon form nor in reduced row-echelon form.

Determine whether each matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form.
⌈ 1 0 0 0 ⌉

| 0 1 1 5 |

⌊ 0 0 0 0 ⌋

• The matrix is in row-echelon form but not in reduced row-echelon form.

• The matrix is not in row-echelon form.

• The matrix is in reduced row-echelon form.

• The matrix is neither in row-echelon form nor in reduced row-echelon form.

Solve the system using Gaussian Elimination with matrices.

2x + 3y + z = 10

2x - 3y - 3z = 22

4x - 2y + 3z = -2

• (5, 2, -6)

• (5, 2, 6)

• (6, 2, 5)

• (2, 5, -6)

Solve the system using Gauss-Jordan elimination with matrices.

-x + y - z = -14

2x - y + z = 21

3x + 2y + z = 19

• (2, 3, 4)

• (4, 3, 7)

• (7, -3, 4)

• (2, -3, 4)

Find 3A - 2B.

A = ⌈ 1 -1 ⌉ B = ⌈2 -1 ⌉

⌊2 -1 ⌋ ⌊-1 8 ⌋

• ⌈ 1 1 ⌉

  ⌊ 8 19 ⌋

• ⌈ -1 -1 ⌉

  ⌊ 8 -19 ⌋

• ⌈ 9 -5 ⌉

  ⌊ 4 -19 ⌋

• ⌈ 8 -19 ⌉

  ⌊ -1 -1 ⌋

Solve for X in the equation X - 3A = -2B.

A = ⌈ -2 -1 ⌉ B = ⌈ 0 3 ⌉

| 1 0 | | 2 0 |

⌊ 3 -4 ⌋ ⌊ -4 -1 ⌋

• ⌈ 6 9 ⌉

  | 1 0 |

  ⌊17 10 ⌋

• ⌈ 6 -3 ⌉

  | -7 0 |

  ⌊-1 14 ⌋

• ⌈ -6 -9 ⌉

  | -1 0 |

  ⌊17 -10 ⌋

• ⌈ 6 3 ⌉

  | 7 0 |

  ⌊1 14 ⌋

Find the product of AB.

A = ⌈ -1 3 ⌉ B = ⌈ 1 2 ⌉

| 4 -5 | ⌊ 0 7 ⌋

⌊ 0 2 ⌋

• not possible

• ⌈ -1 19 4 ⌉

  ⌊ -27 0 14 ⌋

• ⌈ 1 19 ⌉

  | 4 27 |

  ⌊ 0 14 ⌋

• ⌈ -1 19 ⌉

  | 4 -27 |

  ⌊ 0 14 ⌋

Matrix multiplication is NOT _________________

• Commutative

• Associative

• Distributive

• Linear

Is B is the inverse of A?

A = ⌈5 -1 ⌉ B = ⌈-2 1⌉

⌊ 11 -2 ⌋ ⌊-11 5⌋

• yes

• no