Mathematics II2080.110 marksNumerical: linear system consistency conditionSystem of linear equations
What is a system of linear equations? When the system is consistent? Find the condition on g, h, k that makes the system consistent.
What is a system of linear equations? When the system is consistent? Find the condition on g, h, k that makes the system consistent.
$$x_1 - 4x_2 + 7x_3 = g$$ $$3x_2 - 5x_3 = h$$ $$-2x_1 + 5x_2 - 9x_3 = k$$
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System of equations: $$x1 - 4x2 + 7x3 = g \quad (1)$$ $$3x2 - 5x3 = h \quad (2)$$ $$-2x1 + 5x2 - 9x3 = k \quad (3)$$ Coefficient matrix and augmented matrix: $$A = \begin{bmatrix} 1 & -4 & 7 \ 0 & 3 & -5 \ -2 & 5 & -9 \end{bmatrix}, \qquad [A \mid b] = \begin{bmatrix} 1 & -4 & 7 & g \ 0 & 3 & ...