If the system of linear equations (sin theta) | vedclass

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

Question

(D) For a system of linear equations $AX = 0$ to have a non-trivial solution, the determinant of the coefficient matrix $A$ must be zero, i.e.,$|A| =

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(D) For a system of linear equations $AX = 0$ to have a non-trivial solution, the determinant of the coefficient matrix $A$ must be zero, i.e.,$|A| = 0$.Given the system:$(\sin 	heta) x - y + z = 0$$x - (\cos 	heta) y + z = 0$$x + y + (\sin 	heta) z = 0$The determinant is:$|A| = \begin{vmatrix} \sin 	heta & -1 & 1 \ 1 & -\cos 	heta & 1 \ 1 & 1 & \sin 	heta \end{vmatrix} = 0$Expanding along the first row:$\sin 	heta (-\cos 	heta \cdot \sin 	heta - 1) - (-1) (\sin 	heta - 1) + 1 (1 - (-\cos 	heta)) = 0$$-\sin^2 	heta \cos 	heta - \sin 	heta + \sin 	heta - 1 + 1 + \cos 	heta = 0$$-\sin^2 	heta \cos 	heta + \cos 	heta = 0$$\cos 	heta (1 - \sin^2 	heta) = 0$$\cos 	heta (\cos^2 	heta) = 0$$\cos^3 	heta = 0$$\cos 	heta = 0$For the least positive value of $	heta$, $	heta = \frac{\pi}{2}$.

If the system of linear equations $(\sin \theta) x - y + z = 0$, $x - (\cos \theta) y + z = 0$, and $x + y + (\sin \theta) z = 0$ has a non-trivial solution, then the least positive value of $\theta$ is

Similar Questions

The number of solutions of the following system of linear homogeneous equations $x-y+z=0$,$x+2y-z=0$,and $2x+y+3z=0$ is

If $[x]$ denotes the greatest integer $\leq x$,then the system of linear equations
$[\sin \theta ] x + [-\cos \theta ] y = 0$
$[\cot \theta ] x + y = 0$

If $AX=D$ represents the system of simultaneous linear equations $x+y+z=6$,$5x-y+2z=3$ and $2x+y-z=-5$,then $(\operatorname{Adj} A)D=$

The number of values of $k$ for which the system of linear equations,$(k + 2)x + 10y = k$ and $kx + (k + 3)y = k - 1$ has no solution,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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module