Esefcizio 10.7 Sia dato \( S \) il sottoinsieme di \( \mathbb{R}[x] \) definito da \[ S=\{f(x) \in \mathbb{R}[x] \mid f(-1)=f(1)=0, \operatorname{deg} f(x) \leqslant 4\} \cup\{0\} \] sottospazio vettoriale di \( \mathbb{R}[x] \). Determinare la dimensione, la codimensione, una base, equazioni cartesiane, equazioni parametriche ed un complemento per \( S \).

зАданив №2 Дополните выражение до полного квадрата разности и запишите получившийся квадрат разности: \( \quad l^{2}-14 l+()^{2}=( \)

/Evaluate \( :\left(\frac{4^{-8}}{8^{-4}}\right)^{3 / 4} \)

What is the value of one third the determinant of \( \left[\begin{array}{cccc}2 & 3 & 0 & 11 \\ 3 & 5 & -1 & 10 \\ 0 & -6 & 2 & 4 \\ 2 & 4 & 7 & -5\end{array}\right] \) ?

O Functions and Lines Evaluating functions: Linear and quadratic or cubic The functions \( f \) and \( g \) are defined as follows. \[ f(x)=-2 x^{2}-3 \quad g(x)=3 x-1 \] Find \( f(5) \) and \( g(-2) \). Simplify your answers as much as possible. \[ f(5)=\square \] \( g(-2)=\square \)

\( 1 \leftarrow \quad \begin{array}{l}\text { Solve the system of equations by the substitution method. } \\ \begin{aligned} 4 x+2 y & =-154 \\ x-5 y & =0\end{aligned}\end{array} \)