Tables (43)

Table p. 89.0 — 4×3, 1 spanning cell(s)
Alice's lists:
Bob	Cora	Devon
Alice	Alice	Alice
Devon	Bob

columns: Alice's lists: Bob | Alice's lists: Cora | Alice's lists: Devon

Table p. 89.1 — 5×1, 0 spanning cell(s)
Cora's list
Alice
Bob
Cora
Devon

columns: Cora's list

Table p. 89.2 — 5×2, 1 spanning cell(s)
Bob's lists:
Alice	Devon
Bob	Alice
Cora	Bob
Devon

columns: Bob's lists: Alice | Bob's lists: Devon

Table p. 89.3 — 5×2, 1 spanning cell(s)
Devon's lists:
Alice	Bob
Bob	Alice
Cora	Devon
Devon

columns: Devon's lists: Alice | Devon's lists: Bob

Table p. 116.4 — 2×7, 0 spanning cell(s)
Year:	1970	1980	1990	2000	2010	2020
Pop.:	3.70	4.46	5.33	6.14	6.96	7.79

columns: Year: | 1970 | 1980 | 1990 | 2000 | 2010 | 2020

Table p. 188.5 — 9×10, 0 spanning cell(s)
1	1	.	.	.	.	.
-	1	1	1	1
1	1	1	1	1	1
1	1	1	1
1	1	0
1	1	1	1	0
1	1	1	1	0
1	1	1	1	0
.	.	.	.	1	1	1

columns: 1 | | 1 | | . | . | . | . | . | 1

Table p. 190.6 — 4×4, 0 spanning cell(s)
+	0	1	2
0	0	1	2
1	1	2	0
2	2	0	1

columns: + | 0 | 1 | 2

Table p. 190.7 — 4×4, 0 spanning cell(s)
×	1	2
0	0	0
1	1	2
2	2	1

columns: × | 0 | 1 | 2

Table p. 193.8 — 4×5, 0 spanning cell(s)
Value	Color (c)	Shape ( \(p\) )	Shading \((d)\)	Number ( \(n\) )
0	red	diamond	solid	one
1	green	squiggle	striped	two
2	purple	oval	hollow	three

columns: Value | Color (c) | Shape ( \(p\) ) | Shading \((d)\) | Number ( \(n\) )

Table p. 194.9 — 5×5, 0 spanning cell(s)
+	0	1	2	3
0	0	1	2	3
1	1	2	3	0
2	2	3	0	1
3	3	0	1	2

columns: + | 0 | 1 | 2 | 3

Table p. 194.10 — 5×5, 0 spanning cell(s)
×	1	2	3
0	0	0	0
1	1	2	3
2	2	0	2
3	3	2	1

columns: × | 0 | 1 | 2 | 3

Table p. 194.11 — 6×6, 0 spanning cell(s)
+	0	1	2	3	4
0	0	1	2	3	4
1	1	2	3	4	0
2	2	3	4	0	1
3	3	4	0	1	2
4	4	0	1	2	3

columns: + | 0 | 1 | 2 | 3 | 4

Table p. 194.12 — 6×6, 0 spanning cell(s)
×	1	2	3	4
0	0	0	0	0
1	1	2	3	4
2	2	4	1	3
3	3	1	4	2
4	4	3	2	1

columns: × | 0 | 1 | 2 | 3 | 4

Table p. 206.13 — 1×1, 0 spanning cell(s)
\begin{tabular}[t]{l} \(\begin{array}{lllllll}z & s_{1} & s_{2} & s_{3} & x_{1} & x_{2} & x_{3}\end{array}\) \[ \left[\begin{array}{c\|ccc\|ccc\|c} 1 & 0 & 0 & 0 & -2 & -1 & 1 & 0 \\ \hline 0 & 1 & 0 & 0 & -3 & -2 & 2 & 1 \\ 0 & 0 & 1 & 0 & 1 & -1 & 1 & 2 \\ 0 & 0 & 0 & 1 & -1 & 3 & -3 & 3 \end{array}\right] \] \[ \xrightarrow{\substack{R_{1}+2 R_{3} \\ R_{2}+3 R_{3} \\ R_{4}+R_{3}}}\left[\begin{array}{c\|ccc\|ccc\|c} 1 & 0 & 2 & 0 & 0 & -3 & 3 & 4 \\ \hline 0 & 1 & 3 & 0 & 0 & -5 & 5 & 7 \\ 0 & 0 & 1 & 0 & 1 & -1 & 1 & 2 \\ 0 & 0 & 1 & 1 & 0 \uparrow & 2 & -2 & 5 \end{array}\right] . \] \\ new "leading" entry \end{tabular}

columns: \begin{tabular}[t]{l} \(\begin{array}{lllllll}z & s_{1} & s_{2} & s_{3} & x_{1} & x_{2} & x_{3}\end{array}\) \[ \left[\begin{array}{c|ccc|ccc|c} 1 & 0 & 0 & 0 & -2 & -1 & 1 & 0 \\ \hline 0 & 1 & 0 & 0 & -3 & -2 & 2 & 1 \\ 0 & 0 & 1 & 0 & 1 & -1 & 1 & 2 \\ 0 & 0 & 0 & 1 & -1 & 3 & -3 & 3 \end{array}\right] \] \[ \xrightarrow{\substack{R_{1}+2 R_{3} \\ R_{2}+3 R_{3} \\ R_{4}+R_{3}}}\left[\begin{array}{c|ccc|ccc|c} 1 & 0 & 2 & 0 & 0 & -3 & 3 & 4 \\ \hline 0 & 1 & 3 & 0 & 0 & -5 & 5 & 7 \\ 0 & 0 & 1 & 0 & 1 & -1 & 1 & 2 \\ 0 & 0 & 1 & 1 & 0 \uparrow & 2 & -2 & 5 \end{array}\right] . \] \\ new "leading" entry \end{tabular}

Table p. 209.14 — 4×9, 0 spanning cell(s)
0	0	0	-1	-0.8	-1.5	0
1	0	0	0	1	1	100
0	1	0	1	0	1	80	.
0	0	1	1	1	1	150

columns: 1 | 0 | 0 | 0 | -1 | -0.8 | -1.5 | 0 |

Table p. 210.15 — 5×9, 1 spanning cell(s) ⚠ overlap at (1,0); overlap at (4,8)
	\(z\)	\(s_{1}\)	\(s_{2}\)	\(s_{3}\)	\(x_{\mathrm{p}}\)	\(x_{\mathrm{c}}\)	\(x_{\mathrm{pc}}\)
		\(\left[\begin{array}{l}1 \\ \hline 0 \\ 0 \\ 0\end{array}\right.\)	0100	0	0	-1	-0.8	-1.5	0
\(R_{1}+1.5 R_{3}\)	\(\left[\begin{array}{l}1 \\ 0 \\ 0 \\ 0\end{array}\right.\)	0100	1.5 -1 1 -1	0.5	-0.8	0	120
\(\xrightarrow{R_{1}+0.8 R_{2}}\)	\(\left[\begin{array}{l}1 \\ 0 \\ 0 \\ 0\end{array}\right.\)	0.8 1 0 -1	0.7 -1 1 0	0001	-0.3	0	136
\(R_{1}+0.3 R_{4}\)	\(\left[\begin{array}{l}1 \\ 0 \\ 0 \\ 0\end{array}\right.\)	0.5 0 1 -1	0.7 -1 1 0	0.3	0	0	151

columns: | \(z\) | \(s_{1}\) | \(s_{2}\) | \(s_{3}\) | \(x_{\mathrm{p}}\) | \(x_{\mathrm{c}}\) | \(x_{\mathrm{pc}}\) |

Table p. 213.16 — 5×8, 0 spanning cell(s)
	[	00	1	-2	1	-2
\((1 / 2) R_{4}\)	0	0	0	0	1	0
\(R_{1}+2 R_{4}\)	0	1	1/2	0	3/2	-1/2	1
\(R_{2}-R_{4}\)	0	0	-1/2	0	-3/2	-1/2	0
\(R_{3}-R_{4}\)	[	01000	-1/2	1	-1/2	1/2	1

columns: | [ | 00 | 1 | -2 | 1 | -2 |

Table p. 213.17 — 5×6, 5 spanning cell(s) ⚠ overlap at (1,0); overlap at (2,0); overlap at (1,1); overlap at (1,1); overlap at (1,2)
	\(z\)	\(s_{3}\)	\(x_{1}\)	\(x_{2}\)
		[	00100010			\begin{tabular}[t]{l} -1 \\ 0 \\ 0 \\ -1 \\ -1 \\ -1 \end{tabular}	-2	\(\left.0 \begin{array}{l}0 \\ 2 \\ -1 \\ -2\end{array}\right]\)
			00100010
\(R_{1}+R_{2}\)	\(\left[\begin{array}{l}1 \\ 0 \\ 0 \\ 0\end{array}\right.\)	0001	0100	-1	2212
\(R_{1}+R_{2}\)

columns: | \(z\) | \(s_{3}\) | \(x_{1}\) | \(x_{2}\) |

Table p. 214.18 — 2×2, 1 spanning cell(s)
\(\xrightarrow{\substack{(1 / 3) R_{4} \\ R_{1}+R_{4} \\ R_{2}-R_{4}}}\)	\[ \left[\begin{array}{c\|ccc\|cc\|c} 1 & 1 & 0 & 0 & 0 & -1 & 2 \\ \hline 0 & 1 & 0 & 0 & 1 & 1 & 2 \\ 0 & 1 & 1 & 0 & 0 & 0 & 1 \\ 0 & 2 & 0 & 1 & 0 & 3 & 2 \end{array}\right] \]
	\(\left[\begin{array}{c\|ccc\|cc\|c}1 & 5 / 3 & 0 & 1 / 3 & 0 & 0 & 8 / 3 \\ \hline 0 & 1 / 3 & 0 & -1 / 3 & 1 & 0 & 4 / 3 \\ 0 & 1 & 1 & 0 & 0 & 0 & 1 \\ 0 & 2 / 3 & 0 & 1 / 3 & 0 & 1 & 2 / 3\end{array}\right]\)

columns: \(\xrightarrow{\substack{(1 / 3) R_{4} \\ R_{1}+R_{4} \\ R_{2}-R_{4}}}\) | \[ \left[\begin{array}{c|ccc|cc|c} 1 & 1 & 0 & 0 & 0 & -1 & 2 \\ \hline 0 & 1 & 0 & 0 & 1 & 1 & 2 \\ 0 & 1 & 1 & 0 & 0 & 0 & 1 \\ 0 & 2 & 0 & 1 & 0 & 3 & 2 \end{array}\right] \]

Table p. 219.19 — 5×3, 0 spanning cell(s)
Primal	Dual
maximize:	\(x_{1}+2 x_{2}\)	minimize: \(\quad y\)
subject to:	\(-x_{1}+x_{2} \leq 1\)	subject to: \(\quad-y \geq 1\)
\(x_{1}, \quad x_{2} \geq 0\)	\(y \geq 2\)
\(y \geq 0\)

columns: | Primal | Dual

Table p. 219.20 — 5×3, 0 spanning cell(s)
Primal	Dual
maximize:	\(x_{1}+2 x_{2}\)	minimize: \(-y_{1}-y_{2}\)
subject to:	\(x_{1}-x_{2} \leq-1\)	subject to: \(\quad y_{1}-y_{2} \geq 1\)
\(-x_{1}+x_{2} \leq-1\)	\(-y_{1}+y_{2} \geq 2\)
\(x_{1}, \quad x_{2} \geq 0\)	\(y_{1}, \quad y_{2} \geq 0\)

columns: | Primal | Dual

Table p. 219.21 — 5×5, 3 spanning cell(s)
		Primal problem
		Infeasible	Solvable	Unbounded
Dual	Infeasible	✓	.	✓
	Solvable	.	✓	.
	Unbounded	✓	-	.

columns: | | Primal problem Infeasible | Primal problem Solvable | Primal problem Unbounded

Table p. 221.22 — 3×4, 2 spanning cell(s)
Primal problem (maximize)		Dual problem (minimize)
\(i\)-th constraint: \[ \begin{aligned} & \geq \\ & \leq \\ & \leq \end{aligned} \]	\(i\)-th variable: \[ \begin{aligned} & \leq 0 \\ & \text { unc } \\ & \geq 0 \end{aligned} \]
\(j\)-th variable: \[ \begin{aligned} & \geq 0 \\ & \text { unconstrained } \\ & \leq 0 \end{aligned} \]	\(j\)-th constraint: \[ \begin{aligned} & \geq \\ & = \\ & \leq \end{aligned} \]

columns: Primal problem (maximize) \(i\)-th constraint: \[ \begin{aligned} & \geq \\ & \leq \\ & \leq \end{aligned} \] | Primal problem (maximize) | Dual problem (minimize) | Dual problem (minimize) \(i\)-th variable: \[ \begin{aligned} & \leq 0 \\ & \text { unc } \\ & \geq 0 \end{aligned} \]

Table p. 244.23 — 3×3, 0 spanning cell(s)
Algorithm	Resulting form	Matrix decomposition
Gaussian elimination	row echelon form	PLU decomposition
Gauss-Jordan elim.	reduced REF	RREF decomposition

columns: Algorithm | Resulting form | Matrix decomposition

Table p. 366.24 — 7×3, 0 spanning cell(s)
\(\sigma\)	\(\operatorname{sgn}(\sigma)\)	contribution to \(\operatorname{det}(A)\)
(12 3)	1	\(a_{1,1} a_{2,2} a_{3,3}\)
(1 3 2)	-1	\(-a_{1,1} a_{3,2} a_{2,3}\)
(213)	-1	\(-a_{2,1} a_{1,2} a_{3,3}\)
(2 3 1)	1	\(a_{2,1} a_{3,2} a_{1,3}\)
(312)	1	\(a_{3,1} a_{1,2} a_{2,3}\)
(321)	-1	\(-a_{3,1} a_{2,2} a_{1,3}\)

columns: \(\sigma\) | \(\operatorname{sgn}(\sigma)\) | contribution to \(\operatorname{det}(A)\)

Table p. 372.25 — 7×4, 0 spanning cell(s)
\(k\)	\(A \mathbf{v}_{k-1}\)	\(\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)
0	-	-	\(\mathbf{v}_{0}=\mathbf{e}_{1}=(1,0)\)
1	(1.00, 5.00)	5.10	(0.20, 0.98)
2	(2.16,4.90)	5.36	(0.40, 0.92)
3	(2.23, 5.68)	6.10	(0.37, 0.93)
4	(2.23, 5.55)	5.98	(0.37, 0.93)
5	(2.23, 5.57)	6.00	(0.37, 0.93)

columns: \(k\) | \(A \mathbf{v}_{k-1}\) | \(\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\)

Table p. 373.26 — 9×8, 1 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)						\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	( 1.00,	0.00,	0.00,	0.00,	0.00,	0.00)	0.00
1	( 0.00, -0.50,	0.50,	0.00,	0.50,	0.00,	0.50)	-2.00
2	( 0.59,	0.44,	0.29,	0.44,	0.29,	0.00)	-4.26
3	(-0.26,	0.51,	0.32,	0.51,	0.32,	0.00)	-4.83
4	( 0.30,	0.49,	0.37,	0.49,	0.37,	0.08)	-4.91
5	(-0.26,	0.49,	0.37,	0.49,	0.37,	0.09)	-4.91
6	( 0.27,	0.49,	0.38,	0.49,	0.38,	0.10)	-4.92
7	(-0.26,	0.49,	0.38,	0.49,	0.38,	0.10)	-4.92

columns: \(k\) 0 | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) ( 1.00, | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) 0.00, | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) 0.00, | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) 0.00, | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) 0.00, | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) 0.00) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\) 0.00

Table p. 374.27 — 8×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=C \mathbf{v}_{k-1} /\left\\|C \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} C \mathbf{v}_{k}\)
0	(1.00, 0.00, 0.00, 0.00, 0.00, 0.00)	0.00
1	(0.00, 0.00, 0.00, 0.00, 0.00, 1.00)	2.00
2	(0.00, 0.00, 0.00, 0.00, 0.45, 0.89)	1.20
3	(0.00, 0.00, 0.00, 0.33, 0.67, 0.67)	1.33
⋮
26	(0.06, 0.10, 0.17, 0.28, 0.48, 0.81)	1.69
27	(0.06, 0.10, 0.17, 0.28, 0.48, 0.81)	1.68

columns: \(k\) | \(\mathbf{v}_{k}=C \mathbf{v}_{k-1} /\left\|C \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} C \mathbf{v}_{k}\)

Table p. 375.28 — 4×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(1.00, 0.00)	1.00
1	(1.00, 0.00)	1.00
2	(1.00, 0.00)	1.00

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 375.29 — 6×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(0.80, 0.60)	2.68
1	(0.74, 0.67)	2.89
2	(0.72, 0.69)	2.96
3	(0.71, 0.70)	2.99
4	(0.71, 0.71)	3.00

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 376.30 — 5×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(1.00, 0.00)	1.00
1	(0.32, 0.95)	0.40
2	(1.00, 0.00)	1.00
3	(0.32, 0.95)	0.40

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 376.31 — 5×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(0.80, 0.60)	2.20
1	(0.61, 0.79)	1.69
2	(0.80, 0.60)	2.20
3	(0.61, 0.79)	1.69

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 378.32 — 7×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(1.00, 0.00, 0.00)	8.00
1	(0.99, -0.12, 0.00)	8.15
2	(0.99, -0.15, -0.07)	8.19
3	(0.98, -0.20, -0.04)	8.21
4	(0.98, -0.19, -0.10)	8.21
5	(0.97, -0.22, -0.05)	8.21

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 379.33 — 5×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
318	(0.05, 0.43, -0.90)	-8.40
319	(0.00, -0.44, 0.90)	-8.40
320	(0.05, 0.43, -0.90)	-8.41
321	(0.00, -0.44, 0.90)	-8.41

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 380.34 — 6×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(1.00, 0.00, 0.00)	1.00
1	(0.20, 0.78, 0.59)	7.85
2	(0.42, 0.84, 0.33)	8.49
3	(0.36, 0.85, 0.39)	8.53
4	(0.38, 0.85, 0.37)	8.53

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 380.35 — 6×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=B \mathbf{v}_{k-1} /\left\\|B \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} B \mathbf{v}_{k}\)
0	( 1.00, 0.00, 0.00)	-0.21
1	(-0.10, 0.57, 0.81)	-0.52
2	( 0.81, 0.22, -0.54)	-1.81
3	(-0.68, 0.04, 0.73)	-1.99
4	( 0.72, 0.03, -0.69)	-2.00

columns: \(k\) | \(\mathbf{v}_{k}=B \mathbf{v}_{k-1} /\left\|B \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} B \mathbf{v}_{k}\)

Table p. 381.36 — 5×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=C \mathbf{v}_{k-1} /\left\\|C \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} C \mathbf{v}_{k}\)
0	(1.00, 0.00, 0.00)	0.82
1	(0.47, 0.75, 0.46)	0.47
2	(0.51, 0.75, 0.42)	0.47
3	(0.51, 0.75, 0.42)	0.47

columns: \(k\) | \(\mathbf{v}_{k}=C \mathbf{v}_{k-1} /\left\|C \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} C \mathbf{v}_{k}\)

Table p. 381.37 — 2×5, 2 spanning cell(s)
Positive		Not positive
\(\left[\begin{array}{ll}3 & 1 \\ 2 & 7\end{array}\right]\)	\(\left[\begin{array}{lll}2 & 4 & 1 \\ 8 & 1 & 3\end{array}\right]\)	\(\left[\begin{array}{cc}1 & -1 \\ -2 & 3\end{array}\right]\)	\(\left[\begin{array}{lll}4 & 3 & 2 \\ 1 & 0 & 1\end{array}\right]\).

columns: Positive | Positive | | Not positive | Not positive

Table p. 385.38 — 7×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(1.00, 0.00, 0.00)	2.00
1	(0.44, 0.87, 0.22)	4.48
2	(0.52, 0.60, 0.60)	6.96
3	(0.58, 0.56, 0.59)	7.06
4	(0.58, 0.58, 0.58)	7.00
5	(0.58, 0.58, 0.58)	7.00

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 388.39 — 9×3, 0 spanning cell(s)
\(k\)	\(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\\|A \mathbf{v}_{k-1}\right\\|\)	\(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)
0	(1.00, 0.00, 0.00, 0.00, 0.00)	0.00
1	(0.00, 0.71, 0.71, 0.00, 0.00)	0.00
2	(0.94, 0.00, 0.00, 0.24, 0.24)	0.21
3	(0.23, 0.68, 0.68, 0.08, 0.15)	0.49
⋮
16	(0.74, 0.41, 0.41, 0.21, 0.25)	0.99
17	(0.72, 0.44, 0.44, 0.20, 0.24)	1.00
18	(0.74, 0.42, 0.42, 0.21, 0.24)	1.00

columns: \(k\) | \(\mathbf{v}_{k}=A \mathbf{v}_{k-1} /\left\|A \mathbf{v}_{k-1}\right\|\) | \(\mathbf{v}_{k}^{T} A \mathbf{v}_{k}\)

Table p. 410.40 — 7×3, 0 spanning cell(s)
\(n\)	\(F_{n}\)	\(F_{n} / F_{n-1}\)
0	0	-
1	1	-
2	1	1.0000
3	2	2.0000
4	3	1.5000
5	5	1.6667

columns: \(n\) | \(F_{n}\) | \(F_{n} / F_{n-1}\)

Table p. 410.41 — 7×3, 0 spanning cell(s)
\(n\)	\(F_{n}\)	\(F_{n} / F_{n-1}\)
6	8	1.6000
7	13	1.6250
8	21	1.6154
9	34	1.6190
10	55	1.6176
11	89	1.6182

columns: \(n\) | \(F_{n}\) | \(F_{n} / F_{n-1}\)

Table p. 410.42 — 7×3, 0 spanning cell(s)
\(n\)	\(F_{n}\)	\(F_{n} / F_{n-1}\)
12	144	1.6180
13	233	1.6181
14	377	1.6180
15	610	1.6180
16	987	1.6180
17	1597	1.6180

columns: \(n\) | \(F_{n}\) | \(F_{n} / F_{n-1}\)