If 2x + 3y - 5z = 7,x + y + z = 6,and 3x - 4y | vedclass

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

Question

(C) 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

$\left| \begin{array}{ccc} 7 & 3 & -5 \ 6 & 1 & 1 \ 1 & -4 & 2 \end{array} ight| \div \left| \begin{array}{ccc} 2 & 3 & -5 \ 1 & 1 & 1 \ 3 & -4 & 2 \end{array} ight|$

Vedclass · Answer

(C) 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 $x = \frac{D_x}{D}$.Here,$D = \left| \begin{array}{ccc} a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \ a_3 & b_3 & c_3 \end{array} ight| = \left| \begin{array}{ccc} 2 & 3 & -5 \ 1 & 1 & 1 \ 3 & -4 & 2 \end{array} ight|$.And $D_x$ is obtained by replacing the first column of $D$ with the constants $d_1, d_2, d_3$,so $D_x = \left| \begin{array}{ccc} 7 & 3 & -5 \ 6 & 1 & 1 \ 1 & -4 & 2 \end{array} ight|$.Thus,$x = \frac{D_x}{D} = \left| \begin{array}{ccc} 7 & 3 & -5 \ 6 & 1 & 1 \ 1 & -4 & 2 \end{array} ight| \div \left| \begin{array}{ccc} 2 & 3 & -5 \ 1 & 1 & 1 \ 3 & -4 & 2 \end{array} ight|$.

If $2x + 3y - 5z = 7$,$x + y + z = 6$,and $3x - 4y + 2z = 1$,then $x =$

Similar Questions

If $x, y, z$ are all different and not equal to zero and $\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z\end{array}\right|=0$,then the value of $x^{-1}+y^{-1}+z^{-1}$ is equal to

$\left| {\begin{array}{ccc} 19 & 17 & 15 \\ 9 & 8 & 7 \\ 1 & 1 & 1 \end{array}} \right| = $

If $A \neq O$ and $B \neq O$ are $n \times n$ matrices such that $AB = O$,then

Let $\Delta = \left| \begin{array}{ccc} 1 & \omega & 2\omega^2 \\ 2 & 2\omega^2 & 4\omega^3 \\ 3 & 3\omega^3 & 6\omega^4 \end{array} \right|$ where $\omega$ is the cube root of unity,then

The area of $\triangle PQR$ with the vertices $P(k, 1)$,$Q(2, 4)$,and $R(1, 1)$ is $3$ sq. units. Then,$k = $ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module