TU704/3
1. Solve the following system of equations using Gaussian elimination, using a row sum check:
$$3x + 3y + 10z = 48$$
$$5x - 3y + 6z = 8$$
$$6x + 8y + 8z = 70$$
(25%)
2. Solve the following system of equations using Gaussian elimination, using a row sum check:
$$5x + 5y + 10z + 11w = 11$$
$$4x + 2y - 4z + 11w = 33$$
$$6x + 12y + z + 10w = 38$$
$$-2x + 5y + 6z + 6w = -7$$
(45%)
3. Use the Gauss-Jordan technique to find the inverse ($$A^{-1}$$) of the following matrix, using a row sum check:
$$A = \begin{bmatrix} 4 & 4 & -1 \\ 2 & 3 & 4 \\ -1 & -2 & -4 \end{bmatrix}$$
(30%)