antwoorden
Onderstaand overzicht volgt de nummering en de opgaven van de derde editie.
[antwoorden eerste editie | antwoorden tweede editie]
1
| a. De orde van de matrices maken de bewerking onmogelijk. |
| b. $\displaystyle \begin{pmatrix}
-15 & 10 \\
2 & -2 \\
-1 & 2
\end{pmatrix}$ |
| c. $\displaystyle \begin{pmatrix}
46 & 12 & -2 \\
49 & 10 & -7
\end{pmatrix}$ |
| d. $\displaystyle
A \cdot B = \begin{pmatrix}
17 & 46 \\
23 & 40
\end{pmatrix} \; , \;
B \cdot A = \begin{pmatrix}
17 & 46 \\
23 & 40
\end{pmatrix}$ |
| e. $\displaystyle E \cdot F = \begin{pmatrix}
-1 & -2 & -4 \\
0 & 4 & 4 \\
-9 & -6 & -20
\end{pmatrix} \; , \;
F \cdot E = \begin{pmatrix}
2 & -8 & -2 \\
3 & 4 & -5 \\
15 & 0 & -23
\end{pmatrix}$ |
| f. $\displaystyle \begin{pmatrix}
4 & -15 \\
24 & -22
\end{pmatrix}$ |
| g. $\displaystyle \begin{pmatrix}
42 & 40 & -56 \\
6 & 16 & 10
\end{pmatrix}$ |
| h. $\displaystyle \begin{pmatrix}
36 & -16 & -10 \\
-21 & 11 & 6
\end{pmatrix}$ |
| i. De orde van de matrices maken de bewerking onmogelijk. |
2
| a. $\displaystyle k=-10$ |
b. Onmogelijk. |
4
| $\displaystyle a=2 \,,\; b=-2 \,,\; c=4$ |
8
Koppels worden in de vorm $(x,y)$ genoteerd.
| a. $\displaystyle \left\{\left(-2,5\right)\right\}$ |
c. $\displaystyle \left\{\,\right\}$ |
| b. $\displaystyle \left\{\left(0,0\right)\right\}$ |
d. $\displaystyle \left\{\left(0,\tfrac{1}{3}\right)\right\}$ |
9
Drietallen worden in de vorm $(x,y,z)$ genoteerd.
| a. $\displaystyle \left\{\left(\tfrac{2z}{5},\tfrac{9z}{5},z\right) | z \in \mathbb{R}\right\}$ |
d. $\displaystyle \left\{\left(\tfrac{7}{5},-\tfrac{14}{5},\tfrac{13}{5}\right)\right\}$ |
| b. $\displaystyle \left\{\left(\tfrac{2+z}{3},\tfrac{7-7z}{3},z\right) | z \in \mathbb{R}\right\}$ |
e. $\displaystyle \left\{\left(2+5z,5+7z,z\right) | z \in \mathbb{R}\right\}$ |
| c. $\displaystyle \left\{\left(-1,1,-1\right)\right\}$ |
f. $\displaystyle \left\{\,\right\}$ |
10
Viertallen worden in de vorm $(a,b,c,d)$ genoteerd.
| a. $\displaystyle \left\{\left(1,2,3,4\right)\right\}$ |
d. $\displaystyle \left\{\left(\tfrac{6c-d+10}{7},\tfrac{4c-3d-12}{7},c,d\right)| c,d \in \mathbb{R}\right\}$
|
11
Drietallen worden in de vorm $(x,y,z)$ genoteerd.
| a. |
$m \in \mathbb{R} \setminus \left\{-1,5\right\}$ |
$\left\{\,\right\}$ |
|
$m=-1$ |
$\displaystyle \left\{\left(-\tfrac{13+8z}{7},\tfrac{11+10z}{7},z\right) | z \in \mathbb{R}\right\}$ |
|
$m=5$ |
$\displaystyle \left\{\left(\tfrac{35-8z}{7},\tfrac{35+10z}{7},z\right) | z \in \mathbb{R}\right\}$ |
| | | |
| b. |
$m \in \mathbb{R} \setminus \left\{-6,-3\right\}$ |
$\left\{\left(\tfrac{6}{6+m},\tfrac{6-m}{6+m},0\right) |m \in \mathbb{R} \setminus \left\{-6,-3\right\} \right\}$ |
|
$m=-6$ |
$\left\{\,\right\}$ |
|
$m=-3$ |
$\displaystyle \left\{\left(\tfrac{8z+6}{3},\tfrac{7z+9}{3},z\right) | z \in \mathbb{R}\right\}$ |
13
| a. $-4xy$ |
b. $0$ |
c. $0$ |
d. $3\pi-\sqrt{2}$ |
e. $-4x^2y^2z^2$ |
f. $4$ |
14
| a. $\displaystyle \begin{pmatrix}
\tfrac{1}{3} & \tfrac{1}{9} \\
-\tfrac{1}{3} & \tfrac{2}{9}
\end{pmatrix}$ |
c. Niet inverteerbaar. |
| b. Niet inverteerbaar. |
d. $\displaystyle \begin{pmatrix}
27 & 3 & 14 \\
2 & 0 & 1 \\
-17 & -2 & -9
\end{pmatrix}$ |
15
| a. $\displaystyle \begin{pmatrix}
\tfrac{d}{ad-bc} & \tfrac{-b}{ad-bc} \\
\tfrac{-c}{ad-bc} & \tfrac{a}{ad-bc}
\end{pmatrix}$ |
d. $\displaystyle \tfrac{1}{2}\begin{pmatrix}
1 & -2 & 1 \\
0 & 1 & -2 \\
0 & 0 & 1
\end{pmatrix}$ |
| b. $\displaystyle \begin{pmatrix}
0 & 0 & \tfrac{1}{z}\\
0 & \tfrac{1}{y} & 0 \\
\tfrac{1}{x} & 0 & 0
\end{pmatrix}$ |
e. $\displaystyle \tfrac{1}{2}\begin{pmatrix}
4 & -\sqrt{2} \\
-\sqrt{2} & 1
\end{pmatrix}$ |
| c. $\displaystyle \tfrac{6}{5}\begin{pmatrix}
-1 & 2 \\
-4 & 3
\end{pmatrix}$ |
f. $\displaystyle \begin{pmatrix}
0 & \tfrac{1}{2xy} & \tfrac{1}{2xz}\\
\tfrac{1}{2xy} & 0 & \tfrac{1}{2yz} \\
\tfrac{1}{2xz} & \tfrac{1}{2yz} & 0
\end{pmatrix}$ |
16
| 8a. Zie oplossing 8a. |
9a. Geen vierkant stelsel. |
| 8b. Zie oplossing 8b. |
9b. Geen vierkant stelsel. |
| 8c. Determinant is 0. |
9c. Geen vierkant stelsel. |
| 8d. Zie oplossing 8d. |
9d. Zie oplossing 9d. |
|
9e. Determinant is 0. |
|
9f. Determinant is 0. |