Sets of Linear Equations; Determinants
Sets of Linear Equations; Determinants Exercise 1 : Gaussian and Gauss-Jordan elimination Solve the following equations using either Gaussian or Gauss-Jordan elimination. Use matrix notation. $$ \begin{cases} 2x_1 + x_2 + 5x_3 = -21 \\ x_1 + 5x_2 + 2x_3 = 19 \\ 5x_1 + 2x_2 + x_3 = 2 \end{cases} $$ $$ \begin{cases} x - y + 3z = 4 \\ 23x + 2y + 4z = 13 \\ 11.5x + y + 2z = 6.5 \end{cases} $$ $$ \begin{cases} 3x_1 + 2x_2 + x_3 = 49 \\ x_1 + x_2 + x_3 = 8 \\ 5x_1 - 3x_2 + x_3 = 0 \end{cases} $$ $$ \begin{cases} 1.2x - 0.9y + 1.5z = 2.4 \\ 0.8x - 0.5y + 2.5z = 1.8 \\ 1.6x - 1.2y + 2z = 3.2 \end{cases} $$ Exercise 2 : Inverse Matrices Obtain the inverse of the following matrices: ...