b: Đặt \(\overrightarrow{u}=2\overrightarrow{b}-\overrightarrow{c}\)
=>\(\left\{{}\begin{matrix}x_{\overrightarrow{u}}=2\cdot\left(-4\right)-7=-8-7=-15\\y_{\overrightarrow{u}}=2\cdot1-3=-1\end{matrix}\right.\)
Đặt \(3\cdot\overrightarrow{c}=x\cdot\overrightarrow{u}+y\cdot4\overrightarrow{a}\)
=>\(\left\{{}\begin{matrix}x\cdot\left(-15\right)+y\cdot\left(4\cdot5\right)=3\cdot7=21\\x\cdot\left(-1\right)+y\left(4\cdot3\right)=3\cdot3=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-15x+20y=21\\-x+12y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{9}{20}\\y=\dfrac{57}{80}\end{matrix}\right.\)
vậy: \(3\cdot\overrightarrow{c}=\dfrac{-9}{20}\cdot\left(2\overrightarrow{b}-\overrightarrow{c}\right)+\dfrac{57}{80}\cdot4\overrightarrow{a}\)
c: Đặt \(2\overrightarrow{a}-\overrightarrow{d}=x\cdot\overrightarrow{b}+y\cdot\overrightarrow{c}\)
=>\(\left\{{}\begin{matrix}2\cdot5-5=x\cdot\left(-4\right)+y\cdot7\\2\cdot3-0=x\cdot1+y\cdot3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-4x+7y=5\\x+3y=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-4x+7y=5\\4x+12y=24\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-4x+7y+4x+12y=5+24\\x+3y=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}19y=29\\x=6-3y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{29}{19}\\x=6-3\cdot\dfrac{29}{19}=\dfrac{27}{19}\end{matrix}\right.\)
vậy: \(2\overrightarrow{a}-\overrightarrow{d}=\dfrac{27}{19}\cdot\overrightarrow{b}+\dfrac{29}{19}\cdot\overrightarrow{c}\)
a: Đặt \(\overrightarrow{u}=2\overrightarrow{b}+\overrightarrow{c}\)
=>\(\left\{{}\begin{matrix}x_{\overrightarrow{u}}=2\cdot\left(-4\right)+7=-8+7=-1\\y_{\overrightarrow{u}}=2\cdot1+3=5\end{matrix}\right.\)
Đặt \(\overrightarrow{a}=x\cdot\overrightarrow{u}+y\cdot\overrightarrow{d}\)
=>\(\left\{{}\begin{matrix}x\cdot\left(-1\right)+5y=5\\5x+y\cdot0=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{5}\\5y=5+x=5+\dfrac{3}{5}=\dfrac{28}{5}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{3}{5}\\y=\dfrac{28}{25}\end{matrix}\right.\)
vậy: \(\overrightarrow{a}=\dfrac{3}{5}\cdot\left(2\overrightarrow{b}+\overrightarrow{c}\right)+\dfrac{28}{25}\cdot\overrightarrow{d}\)
