Let λand α be real. The set of all values of for which the system of linear equationsλ$$x+($$$$sin$$α$$)y+($$$$cos$$α$$)z=0$$,$$x+($$$$cos$$α$$)y+($$$$sin$$α$$)z=0$$,−$$x+($$$$sin$$α$$)y$$−$$($$$$cos$$α$$)z=0has$$ a $$non-trival$$ solution is

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Let λand α be real. The set of all values of for which the system of linear equationsλ$$x+($$$$sin$$α$$)y+($$$$cos$$α$$)z=0$$,$$x+($$$$cos$$α$$)y+($$$$sin$$α$$)z=0$$,−$$x+($$$$sin$$α$$)y$$−$$($$$$cos$$α$$)z=0has$$ a $$non-trival$$ solution is

Infinity Learn · Accepted Answer

The condition for a homogeneour system of equations to have a $$non-trivial$$ solution is Δ$$=0$$ ⇒Δ$$=$$λ$$sin$$α$$cos$$α$$1cos$$α$$sin$$α$$-1sin$$α$$-$$$$cos$$α$$=0$$ ⇒λ$$-cos2$$α$$-sin2$$α$$-$$$$sin$$α$$-$$$$cos$$α$$+$$$$sin$$α$$+$$$$cos$$α$$sin$$α$$+$$$$cos$$α$$=0$$ ⇒λ$$=cos2$$α$$+sin2$$α The range of $$cos2$$α$$+sin2$$α is $$-2$$,$$2$$. ∴The range of λ is $$-2$$,$$2$$

Let $λ$ and $α$ be real. The set of all values of for which the system of linear equations $λ x + (\sin α) y + (\cos α) z = 0$ , $x + (\cos α) y + (\sin α) z = 0$ , $- x + (\sin α) y - (\cos α) z = 0$ has a non-trival solution is

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Let λand α be real. The set of all values of for which the system of linear equationsλx+(sinα)y+(cosα)z=0,x+(cosα)y+(sinα)z=0,−x+(sinα)y−(cosα)z=0has a non-trival solution is

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Let $λ$ and $α$ be real. The set of all values of for which the system of linear equations $λ x + (\sin α) y + (\cos α) z = 0$ , $x + (\cos α) y + (\sin α) z = 0$ , $- x + (\sin α) y - (\cos α) z = 0$ has a non-trival solution is