The system of equations 4x + y - 2z = 0,x - 2 | vedclass

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

Question

(C) The given system of homogeneous linear equations is:$4x + y - 2z = 0$$x - 2y + z = 0$$x + y - z = 0$To check for the nature of the solution,we cal

Vedclass · Accepted Answer

non-trivial solution

Vedclass · Answer

(C) The given system of homogeneous linear equations is:$4x + y - 2z = 0$$x - 2y + z = 0$$x + y - z = 0$To check for the nature of the solution,we calculate the determinant $D$ of the coefficient matrix:$D = \begin{vmatrix} 4 & 1 & -2 \ 1 & -2 & 1 \ 1 & 1 & -1 \end{vmatrix}$Expanding along the first row:$D = 4((-2)(-1) - (1)(1)) - 1((1)(-1) - (1)(1)) - 2((1)(1) - (-2)(1))$$D = 4(2 - 1) - 1(-1 - 1) - 2(1 + 2)$$D = 4(1) - 1(-2) - 2(3)$$D = 4 + 2 - 6 = 0$Since the determinant $D = 0$,the system of homogeneous equations has non-trivial solutions (infinitely many solutions).

The system of equations $4x + y - 2z = 0$,$x - 2y + z = 0$,and $x + y - z = 0$ has

Similar Questions

Solve the system of linear equations using the matrix method: $x-y+z=4$,$2x+y-3z=0$,and $x+y+z=2$.

The number of values of $\alpha$ for which the system of equations: $x+y+z=\alpha$,$\alpha x+2 \alpha y+3 z=-1$,and $x+3 \alpha y+5 z=4$ is inconsistent,is:

If the system of equations $x+y+z=2$,$2x+4y-z=6$,and $3x+2y+\lambda z=\mu$ has infinitely many solutions,then:

Examine the consistency of the system of equations: $x+2y=2$ and $2x+3y=3$.

For the system of equations $x+y+z=6$,$x+2y+\alpha z=10$,and $x+3y+5z=\beta$,which one of the following is $NOT$ true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module