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To solve the given linear system numerically using Cramer's Rule, let's first check the conditions for the rule to apply. Cramer's Rule can be used when the following two conditions hold: 1. The system of linear equations must have the same number of equations as unknowns. In other words, the system should be square, i.e., the coefficient matrix should be a square matrix (3x3 in this case). 2. The determinant of the coefficient matrix must be non-zero. If the determinant is zero, Cramer's Rule cannot be used, and the system may either have no solution or infinitely many solutions. ### Given System: We have the following linear system of equations: 1. \( 2x - 3y + 4z = 20\frac{2}{5} \) 2. \( x + 2y - 3z + 13.4 = 0 \) 3. \( -x - 2y + 5z = \frac{113}{6} \) ### Step 1: Convert to standard form To make it easier to solve, let's first rewrite the equations in standard form (Ax + By + Cz = D): 1. \( 2x - 3y + 4z = 20\frac{2}{5} = \frac{102}{5} \) 2. \( x + 2y - 3z = -13.4 = -\frac{67}{5} \) 3. \( -x - 2y + _____ __________ _______ ____ __________ _________.
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