Question

Vector form

Answer 1

How har I write this equation in vector form?
x1=-x2
x3=(1/2)x4

Answer 2

A vector \(\vec{v}\in\mathbb{R}^4\) has four components, and can be written as \(\vec{v}=\langle x_1,x_2,x_3,x_4\rangle\).

Given that
\[\begin{cases}
x_1=-x_2\\
x_3=\frac{1}{2}x_4
\end{cases}\]
you can substitute the components accordingly:
\[\vec{v}=\langle x_1,x_2,x_3,x_4\rangle=\left\langle -x_2,x_2,\frac{1}{2}x_4,x_4 \right\rangle\]
To make it look a bit cleaner, let \(a=x_2,b=x_4\), where \(a,b\in\mathbb{R}\):
\[\vec{v}=\left\langle -a,a,\frac{1}{2}b,b\right\rangle\]
There are other ways to write \(\vec{v}\), depending on how you manipulate the given equations.

Answer 3

Thanks..