Question

E4❤
Va rog frumos sa ma ajutati!

Answer 1

$\displaystyle \mathtt{E4.~~~A=\left(\begin{array}{ccc}\mathtt{2x}&\mathtt{4y}&\mathtt{3z}\\\mathtt1&\mathtt {u}&\mathtt{-4}\\\mathtt{-v}&\mathtt{-2v}&\mathtt{t+3}\end{array}\right);~B= \left(\begin{array}{ccc}\mathtt1&\mathtt z&\mathtt v\\\mathtt{-y}&\mathtt {-v}&\mathtt x\\\mathtt{-x}&\mathtt{2y}&\mathtt{x-z}\end{array}\right);}\\\\ \mathtt{ C=\left(\begin{array}{ccc}\mathtt3&\mathtt{-2}&\mathtt3\\\mathtt2&\mathtt 3&\mathtt{-3}\\\mathtt2&\mathtt4&\mathtt2\end{array}\right)}$

$\displaystyle \mathtt{x,~y,~z,~u,~v,~t=?~~~~~~~~~~~~~~~~~~~~A+B=C}$

$\displaystyle \mathtt{A+B=\left(\begin{array}{ccc}\mathtt{2x}&\mathtt{4y}&\mathtt{3z}\\\mathtt1&\mathtt {u}&\mathtt{-4}\\\mathtt{-v}&\mathtt{-2v}&\mathtt{t+3}\end{array}\right)+\left(\begin{array}{ccc}\mathtt1&\mathtt z&\mathtt v\\\mathtt{-y}&\mathtt {-v}&\mathtt x\\\mathtt{-x}&\mathtt{2y}&\mathtt{x-z}\end{array}\right)=}\\\\ \mathtt{=\left(\begin{array}{ccc}\mathtt{2x+1}&\mathtt{4y+z}&\mathtt {3z+v}\\\mathtt{1-y}&\mathtt{u-v}&\mathtt{-4+x}\\\mathtt{-v-x}&\mathtt{-2v+2y}&\mathtt{t+3+x-z}\end{array}\right)}$

$\displaystyle \mathtt{\left(\begin{array}{ccc}\mathtt{2x+1}&\mathtt{4y+z}&\mathtt {3z+v}\\\mathtt{1-y}&\mathtt{u-v}&\mathtt{-4+x}\\\mathtt{-v-x}&\mathtt{-2v+2y}&\mathtt{t+3+x-z}\end{array}\right)=\left(\begin{array}{ccc}\mathtt3&\mathtt{-2}&\mathtt3\\\mathtt2&\mathtt 3&\mathtt{-3}\\\mathtt2&\mathtt4&\mathtt2\end{array}\right)}$

$\displaystyle \mathtt{2x+1=3\Rightarrow 2x=3-1\Rightarrow 2x=2\Rightarrow \boxed{\mathtt{x=1}}}\\ \\ \mathtt{1-y=2\Rightarrow -y=2-1\Rightarrow -y=1\Rightarrow \boxed{\mathtt{y=-1}}}\\ \\ \mathtt{4y+z=-2\Rightarrow4 \cdot (-1)+z=-2\Rightarrow -4+z=-2\Rightarrow z=-2+4\Rightarrow }\\ \\ \mathtt{\Rightarrow \boxed{\mathtt{z=2}}}\\ \\ \mathtt{-v-x=2\Rightarrow -v-1=2\Rightarrow -v=2+1\Rightarrow -v=3\Rightarrow \boxed{\mathtt{v=-3}}}$

$\displaystyle \mathtt{u-v=3\Rightarrow u-(-3)=3\Rightarrow u+3=3\Rightarrow u=3-3\Rightarrow \boxed{\mathtt{u=0}}} \\ \\ \mathtt{t+3+x-z=2\Rightarrow t+3+1-2=2\Rightarrow t+2=2 \Rightarrow t=2-2\Rightarrow }\\ \\ \mathtt{\Rightarrow \boxed{\mathtt{t=0}}}\\ \\ \mathtt{x=1;~y=-1;~z=2;~u=0;~v=-3;~t=0}$