Question \#3: \( \left\{\begin{array}{l}x-2 y+3 z=-25 \\ x-2 y-3 z=5 \\ 5 x+2 y-3 z=17\end{array} \quad\right. \) Use cramers rule to

Cramer's Rule is a powerful method for solving systems of linear equations using determinants. To apply it, you'll need to calculate the determinant of the coefficient matrix and the determinants of matrices formed by replacing columns with the constants on the right-hand side. In this case, you would form a \(3 \times 3\) matrix from the coefficients of \(x\), \(y\), and \(z\), and then compute the necessary determinants to find values for \(x\), \(y\), and \(z\). A common mistake when using Cramer's Rule is forgetting to correctly substitute the right column in your determinant calculation. Make sure you double-check your matrices before calculating the determinants! Additionally, ensure that the original coefficient matrix is invertible, which means its determinant should not equal zero—otherwise, the system has no unique solution. Happy calculating!