- same ✔
- different

- A is transpose of B
- A is inverse of B ✔
- A is singular
- B is singular

- False
- True ✔

- -4 ✔
- 3
- 2
- 1

- -2x+7x+2x=5, 6x-2x+3x=1, x+x-5x=-13
- -2x+7x+2x=5, 6x-2x+3x=1, x+x-5x=-13
- x+x-5x=-13, 6x-2x+3x=1, -2x+7x+2x=5
- 6x-2x+3x=1, -2x+7x+2x=5, x+x-5x=-13

- Cos(theta), -Cos(theta)
- Sin(theta), Cos(theta)
- Sin(theta), -Sin(theta)
- -Sin(theta), Cos(theta)

- one
- two
- three
- four

- -x+12x+5x=8, 9x+5x-3x=12, 2x-4x+7x=-15
- 9x+5x-3x=12, -x+12x+5x=8, 2x-4x+7x=-15
- 2x-4x+7x=-15, -x+12x+5x=8, 9x+5x-3x=12
- 9x+5x-3x=12, 2x-4x+7x=-15, -x+12x+5x=8

- Smallest
- Largest ✔

- True ✔
- False

- same ✔
- different

- True ✔
- False

- True ✔
- False

- exists, unique ✔
- exists, consistent
- trivial, unique
- nontrivial, inconsistent

- independent ✔
- dependent

- Stable
- Unstable
- Convergent ✔
- Divergent

A = [ | 1 | 1/4 | 1/3 | ] |

1/4 | 1/3 | 1/2 | ||

1/3 | 1/2 | 1/5 |

- tan 2Θ = 2a
_{13}/a_{11}-a_{33}✔

A = [ | 1 | 1/4 | 1/2 | ] |

1/4 | 1/3 | 1/4 | ||

1/2 | 1/4 | 1/5 |

S _{1}= [cos 0.4480 0 -sin 0.4480 ] ✔ 0 1 0 sin 0.4480 0 cos 0.4480

- Easiest
- Complicated ✔

- x = 3 - 2y - 2z, y = 2/3 - x/3 - z, z = 2/5 - x/5 - y/5

- True ✔
- False

A = [ | 1 | 1/4 | 1/3 | ] |

1/4 | 1/3 | 1/2 | ||

1/3 | 1/2 | 1/5 |

S _{1}= [cos 0.7191 0 -sin 0.7191 ] ✔ 0 1 0 sin 0.7191 0 cos 0.7191

- no solution
- unique ✔
- infinite many
- finite many

- The system has unique solution ✔
- The system has finite multiple solutions
- The system has infinite many solutions
- The system has no solution

_{i}

^{(r+1)}replaces those of x

_{i}

^{r}as soon as they become available

- True
- False ✔

- Inverse
- Square
- Identity ✔
- None

- True ✔
- False

_{1}- 2x

_{2}+ 3x

_{3}= 1

_{1}+ 7x

_{2}+ 2x

_{3}= 5

_{1}+ x

_{2}- 5x

_{3}= -13

- dx
_{3}= R_{3}/a_{33}✔

_{23}| be the numerically largest off-diagonal element then using Jacobi's method the value of theta can be found by

- tan 2 Θ = 2a
_{23}/a_{22}-a_{33 }✔

- unique
- no solution ✔
- infinite many
- finite many

^{x}-5=0 is bounded in the interval

- [-2, 1]
- [-1, 1]
- [0, 1] ✔
- [1, 2]

x y Δy Δ ^{2}y0.1 0.003 0.145 0.077 0.5 0.148 0.222 ✔ 0.9 0.37

- Jacobi's
- Gauss-Seidel
- Relaxation
- Gaussian elimination ✔

- a unique solution ✔
- many solutions
- infinite many solutions
- None

- same ✔
- different

- Indirect
- Iterative ✔
- Jacobi
- None

x y Δy Δ ^{2}y0.1 0.003 0.245 0.204 0.7 0.248 0.449 ✔ 1.3 0.697

- (2, 3)
- (3, -2)
- (-2, 3)
- (1, 4) ✔