Solve the Matrix Equation [[3g,h^2],[4,-2f]]=[[-12,81],[4,3f]]

$[\begin{array}{c} 3 g & h^{2} \\ 4 & - 2 f \end{array}] = [\begin{array}{c} - 12 & 81 \\ 4 & 3 f \end{array}]$

Step 1

Write as a linear system of equations.

$3 g = - 12 h^{2} = 81 4 = 4 - 2 f = 3 f$

Step 2

Since $4 = 4$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.