Solve MV=-mv

$$M V = - m v$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=-\frac{mv}{V}\text{, }&V\neq 0\\M\in \mathrm{C}\text{, }&\left(m=0\text{ or }v=0\right)\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$MV=-mv$$

The equation is in standard form.

$$VM=-mv$$

Divide both sides by V.

$$\frac{VM}{V}=-\frac{mv}{V}$$

Dividing by V undoes the multiplication by V.

$$M=-\frac{mv}{V}$$

Solve for V (complex solution)

$$\left\{\begin{matrix}V=-\frac{mv}{M}\text{, }&M\neq 0\\V\in \mathrm{C}\text{, }&\left(m=0\text{ or }v=0\right)\text{ and }M=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$MV=-mv$$

Divide both sides by M.

$$\frac{MV}{M}=-\frac{mv}{M}$$

Dividing by M undoes the multiplication by M.

$$V=-\frac{mv}{M}$$

Solve for M

$$\left\{\begin{matrix}M=-\frac{mv}{V}\text{, }&V\neq 0\\M\in \mathrm{R}\text{, }&\left(m=0\text{ or }v=0\right)\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$MV=-mv$$

The equation is in standard form.

$$VM=-mv$$

Divide both sides by V.

$$\frac{VM}{V}=-\frac{mv}{V}$$

Dividing by V undoes the multiplication by V.

$$M=-\frac{mv}{V}$$

Solve for V

$$\left\{\begin{matrix}V=-\frac{mv}{M}\text{, }&M\neq 0\\V\in \mathrm{R}\text{, }&\left(m=0\text{ or }v=0\right)\text{ and }M=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$MV=-mv$$

Divide both sides by M.

$$\frac{MV}{M}=-\frac{mv}{M}$$

Dividing by M undoes the multiplication by M.

$$V=-\frac{mv}{M}$$