Solve L_{1}L_{2}=L_{1}L_{T}

$$L _ { 1 } L _ { 2 } = L _ { 1 } L _ { T }$$

Solve for L_1

$$\left\{\begin{matrix}\\L_{1}=0\text{, }&\text{unconditionally}\\L_{1}\in \mathrm{R}\text{, }&L_{2}=L_{T}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract L_{1}L_{T} from both sides.

$$L_{1}L_{2}-L_{1}L_{T}=0$$

Combine all terms containing L_{1}.

$$\left(L_{2}-L_{T}\right)L_{1}=0$$

Divide 0 by L_{2}-L_{T}.

$$L_{1}=0$$

Solve for L_2

$$\left\{\begin{matrix}\\L_{2}=L_{T}\text{, }&\text{unconditionally}\\L_{2}\in \mathrm{R}\text{, }&L_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$L_{1}L_{2}=L_{1}L_{T}$$

Divide both sides by L_{1}.

$$\frac{L_{1}L_{2}}{L_{1}}=\frac{L_{1}L_{T}}{L_{1}}$$

Dividing by L_{1} undoes the multiplication by L_{1}.

$$L_{2}=\frac{L_{1}L_{T}}{L_{1}}$$

Divide L_{1}L_{T} by L_{1}.

$$L_{2}=L_{T}$$