Matrix Operations and Systems of Equations

Matrix Operations and Inverse Properties

• Matrix Addition Compatibility: The addition $B + C$ is not possible because the matrices have different dimensions.
• Matrix Subtraction: The expression $C - 2A$ involves scalar multiplication of matrix $A$ followed by matrix subtraction.
• Inverse Matrix Existence: Matrix $D^{-1}$ existence depends on determinant conditions; a crossed-out note regarding negative matrix elements is noted as incorrect.

Systems of Equations

• First System:

  • $2x - y$
  • $x y = 4$

• Second System:

  • $x^2 + x y + y^2 = 84$
  • $4x - y = 0$
  • $4x^3 - y = 0$