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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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:

Similar Questions

The linear system of equations $\begin{cases} 8x - 3y - 5z = 0 \\ 5x - 8y + 3z = 0 \\ 3x + 5y - 8z = 0 \end{cases}$ has

The existence of the unique solution of the system of equations $2x + y + z = \beta$,$10x - y + \alpha z = 10$ and $4x + 3y - z = 6$ depends on

If the system of linear equations $x + y + z = 5$,$x + 2y + 2z = 6$,and $x + 3y + \lambda z = \mu$ (where $\lambda, \mu \in \mathbb{R}$) has infinitely many solutions,then the value of $\lambda + \mu$ is:

The system of linear equations $\lambda x + y + z = 3$,$x - y - 2z = 6$,and $-x + y + z = \mu$ has:

Let $(x, y, z)$ be points with integer coordinates satisfying the system of homogeneous equations:
$3x - y - z = 0$,$-3x + z = 0$,$-3x + 2y + z = 0$.
Then the number of such points for which $x^2 + y^2 + z^2 \leq 100$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module