The number of solutions of the following equa | vedclass

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

Question

(A) The given system of linear equations is:$0x_1 + 1x_2 - 1x_3 = 1$$-1x_1 + 0x_2 + 2x_3 = -2$$1x_1 - 2x_2 + 0x_3 = 3$First,we calculate the determina

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) The given system of linear equations is:$0x_1 + 1x_2 - 1x_3 = 1$$-1x_1 + 0x_2 + 2x_3 = -2$$1x_1 - 2x_2 + 0x_3 = 3$First,we calculate the determinant $D$ of the coefficient matrix:$D = \begin{vmatrix} 0 & 1 & -1 \ -1 & 0 & 2 \ 1 & -2 & 0 \end{vmatrix} = 0(0 - (-4)) - 1(0 - 2) + (-1)(2 - 0) = 0 + 2 - 2 = 0$Since $D = 0$,the system is either inconsistent or has infinitely many solutions. We calculate $D_1$ by replacing the first column with the constants:$D_1 = \begin{vmatrix} 1 & 1 & -1 \ -2 & 0 & 2 \ 3 & -2 & 0 \end{vmatrix} = 1(0 - (-4)) - 1(0 - 6) + (-1)(4 - 0) = 4 + 6 - 4 = 6$Since $D = 0$ and $D_1 
eq 0$,the system of equations is inconsistent and has no solution.

The number of solutions of the following equations $x_2 - x_3 = 1$,$-x_1 + 2x_3 = -2$,$x_1 - 2x_2 = 3$ is

Similar Questions

The system of linear equations $x + y + z = 2$,$2x + y - z = 3$,and $3x + 2y + kz = 4$ has a unique solution if

If the system of equations $x + ay = 0,$ $az + y = 0$ and $ax + z = 0$ has infinite solutions,then the value of $a$ is

If the system of linear equations $2x + 2y + 3z = a$,$3x - y + 5z = b$,and $x - 3y + 2z = c$,where $a, b, c$ are non-zero real numbers,has more than one solution,then:

If $A$ and $B$ are the two real values of $k$ for which the system of equations $x+2y+z=1$,$x+3y+4z=k$,and $x+5y+10z=k^2$ is consistent,then $A+B=$

Let the system of equations $x+2y+3z=5$,$2x+3y+z=9$,and $4x+3y+\lambda z=\mu$ have an infinite number of solutions. Then $\lambda+2\mu$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module