Given the system of linear equations: 2x + 3y | vedclass

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Question

(A) According to Cramer's Rule,for a system of linear equations $a_1x + b_1y + c_1z = d_1$,$a_2x + b_2y + c_2z = d_2$,and $a_3x + b_3y + c_3z = d_3$,t

Vedclass · Accepted Answer

$\frac{\begin{vmatrix} 9 & 3 & 4 \ 10 & 9 & 3 \ 11 & 10 & 5 \end{vmatrix}}{\begin{vmatrix} 2 & 3 & 4 \ 4 & 9 & 3 \ 5 & 10 & 5 \end{vmatrix}}$

Vedclass · Answer

(A) According to Cramer's Rule,for a system of linear equations $a_1x + b_1y + c_1z = d_1$,$a_2x + b_2y + c_2z = d_2$,and $a_3x + b_3y + c_3z = d_3$,the value of $x$ is given by $x = \frac{D_1}{D}$.Here,$D$ is the determinant of the coefficient matrix:$D = \begin{vmatrix} 2 & 3 & 4 \ 4 & 9 & 3 \ 5 & 10 & 5 \end{vmatrix}$.$D_1$ is the determinant obtained by replacing the first column of $D$ with the constants $d_1, d_2, d_3$:$D_1 = \begin{vmatrix} 9 & 3 & 4 \ 10 & 9 & 3 \ 11 & 10 & 5 \end{vmatrix}$.Thus,$x = \frac{D_1}{D} = \frac{\begin{vmatrix} 9 & 3 & 4 \ 10 & 9 & 3 \ 11 & 10 & 5 \end{vmatrix}}{\begin{vmatrix} 2 & 3 & 4 \ 4 & 9 & 3 \ 5 & 10 & 5 \end{vmatrix}}$.Therefore,option $A$ is the correct answer.

Given the system of linear equations: $2x + 3y + 4z = 9$,$4x + 9y + 3z = 10$,and $5x + 10y + 5z = 11$. The value of $x$ is given by:

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