Exercise 1.1.31

Question

Write down three equations for $c, d, e$ so that $c u+d v+e w=b .$ Can you somehow find $c, d, e$ for this $b$ ?
$$
\boldsymbol{u}=\left[\begin{array}{r}
2 \
-1 \
0
\end{array}ight] \quad \boldsymbol{v}=\left[\begin{array}{r}
-1 \
2 \
-1
\end{array}ight] \quad \boldsymbol{w}=\left[\begin{array}{r}
0 \
-1 \
2
\end{array}ight] \quad \boldsymbol{b}=\left[\begin{array}{l}
1 \
0 \
0
\end{array}ight]
$$

Prakash Anand · Accepted Answer

The equations $c \boldsymbol{u}+d \boldsymbol{v}+e \boldsymbol{w}=\boldsymbol{b}$ are

$$\begin{array}{rlrlr}
2c - d      & =1 &\quad 	ext{so}\    &d=2 e & c=3 / 4 \
-c + 2d - e & =0 &\quad  	ext{then}\ &c=3 e & d=2 / 4 \
-d + 2e     & =0 &\quad 	ext{then}\  &4 e=1 & e=1 / 4
\end{array}$$

Exercise 1.1.31

Answers

Comments

Exercise 1.1.31

Answers

Comments

Add answer