Linear Algebra, 5th Edition

Section 6.3

1. 1.

   1. (a) T

   2. (b) F

   3. (c) F

   4. (d) T

   5. (e) F

   6. (f) T

   7. (g) T

2. 2.

   1. (a) $y=(1,-2,4)$

   2. (c) $y=210x^2-204x+33$

3. 3.

   1. (a) ${\text{T}}^{*}(x)=(11,-12)$

   2. (c) ${\text{T}}^{*}(f(t))=12+6t$

4. 14. ${\text{T}}^{*}(x)=\langle x,z\rangle y$

5. 20.

   1. (a) The linear function is$y=-2t+5/2$ with $E=1$ and the quadratic function is $y=t^2/3-4t/3+2$ with $E=0.$

   2. (b) The linear function is $y=1.25t+0.55$ with $E=0.3,$ and the quadratic function is $t^2/56+15t/14+239/280$ with $E=0.22857$(approximation).

6. 21. The spring constant is approximately 2.1.

7. 22.

   1. (a) $x={\displaystyle \frac{2}{7}},y={\displaystyle \frac{3}{7}},z={\displaystyle \frac{1}{7}}$

   2. (d) $x={\displaystyle \frac{7}{12}},y={\displaystyle \frac{1}{12}},z={\displaystyle \frac{1}{4}},w=-{\displaystyle \frac{1}{12}}$