Esencrio 15.9 Una forma bilineare $$ b $$ di $$ \mathbb{R}^{2} $$ ha come matrice associata rispetto alla base $$ B=\{(1,1),(-1,-2)\} $$ la matrice $$ \left.\qquad \begin{array}{cc}1 & -2 \ -2 & 5\end{array} ight) $$ (i) Calcolare $$ b((1,1),(1,1)) $$ e $$ b((1,-1),(2,7)) $$. (ii) Calcolare $$ b\left((x, y, z),\left(x^{\prime}, y^{\prime}, z^{\prime} ight) ight) $$, per due generici vettori $$ (x, y, z) $$ e $$ \left(x^{\prime}, y^{\prime}, z^{\prime} ight) $$ dì $$ \mathbb{R}^{3} $$.

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Esencrio 15.9 Una forma bilineare $$ b $$ di $$ \mathbb{R}^{2} $$ ha come matrice associata rispetto alla base $$ B=\{(1,1),(-1,-2)\} $$ la matrice $$ \left.\qquad \begin{array}{cc}1 & -2 \ -2 & 5\end{array}ight) $$ (i) Calcolare $$ b((1,1),(1,1)) $$ e $$ b((1,-1),(2,7)) $$. (ii) Calcolare $$ b\left((x, y, z),\left(x^{\prime}, y^{\prime}, z^{\prime}ight)ight) $$, per due generici vettori $$ (x, y, z) $$ e $$ \left(x^{\prime}, y^{\prime}, z^{\prime}ight) $$ dì $$ \mathbb{R}^{3} $$.

Brewer Weber · Accepted Answer

- Calcolare $$ b((1,1),(1,1)) $$ e $$ b((1,-1),(2,7)) $$. - $$ b((1,1),(1,1)) = 2 $$ - $$ b((1,-1),(2,7)) = 36 $$ - Calcolare $$ b\left((x, y, z),\left(x^{\prime}, y^{\prime}, z^{\prime}\right)\right) $$. - $$ b((x,y,z),(x',y',z')) $$ può essere calcolato usando le coordinate rispetto alla base $$ B $$.

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