Question

Solve the following system of equations using Cramer's rule. 

 

x + y - z = 6

 

3x - 2y + z = -5

 

x + 3y - 2z = 14

16 Nov 2025
Answer :
Word Count : 395
To solve the given system of equations using Cramer's rule, first write the coefficient matrix A: [ A = \begin{bmatrix} 1 & 1 & -1 \ 3 & -2 & 1 \ 1 & 3 & -2 \end{bmatrix} ] and the constant matrix B: [ B = \begin{bmatrix} 6 \ -5 \ 14 \end{bmatrix} ] The determinant of A, (|A|), is calculated using the formula for a 3×3 determinant: [ |A| = 1((-2)(-2) - (1)(3)) - 1(3(-2) - (1)(1)) _________ _______ ____ _________ _____ _____ ________.
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