Linear Algebra Exercises-n-Answers.pdf
Linear Algebra Exercises-n-Answers.pdf
Linear Algebra Exercises-n-Answers.pdf
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<strong>Answers</strong> to <strong>Exercises</strong> 145<br />
2 With this input<br />
⎛ ⎞<br />
1 1852.71<br />
1 1858.88<br />
A =<br />
⎜.<br />
.<br />
⎟<br />
⎝1 1985.54⎠<br />
1 1993.71<br />
⎛ ⎞<br />
292.0<br />
285.0<br />
b =<br />
⎜ .<br />
⎟<br />
⎝226.32⎠<br />
224.39<br />
(the dates have been rounded to months, e.g., for a September record, the decimal .71 ≈ (8.5/12) was<br />
used), Maple responded with an intercept of b = 994.8276974 and a slope of m = −0.3871993827.<br />
280<br />
260<br />
240<br />
220<br />
3 With this input (the years are zeroed at 1900)<br />
⎛ ⎞<br />
1 .38<br />
1 .54<br />
A :=<br />
⎜..<br />
⎟<br />
⎝1 92.71⎠<br />
1 95.54<br />
1850 1900 1950 2000<br />
⎛ ⎞<br />
249.0<br />
246.2<br />
b =<br />
⎜ .<br />
⎟<br />
⎝208.86⎠<br />
207.37<br />
(the dates have been rounded to months, e.g., for a September record, the decimal .71 ≈ (8.5/12) was<br />
used), Maple gives an intercept of b = 243.1590327 and a slope of m = −0.401647703. The slope given<br />
in the body of this Topic for the men’s mile is quite close to this.<br />
250<br />
240<br />
230<br />
220<br />
210<br />
4 With this input (the years are zeroed at 1900)<br />
⎛ ⎞<br />
1 21.46<br />
1 32.63<br />
A =<br />
. .<br />
⎜.<br />
.<br />
⎟<br />
⎝1 89.54⎠<br />
1 96.63<br />
200<br />
1900 1920 1940 1960 1980 2000<br />
⎛ ⎞<br />
373.2<br />
327.5<br />
b =<br />
.<br />
⎜ .<br />
⎟<br />
⎝255.61⎠<br />
252.56<br />
(the dates have been rounded to months, e.g., for a September record, the decimal .71 ≈ (8.5/12) was<br />
used), MAPLE gave an intercept of b = 378.7114894 and a slope of m = −1.445753225.<br />
380<br />
360<br />
340<br />
320<br />
300<br />
280<br />
260<br />
240<br />
220<br />
1900 1920 1940 1960 1980 2000
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