JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations
\(\begin{aligned} & (\lambda-1) x+(\lambda-4) y+\lambda z=5 \\ & \lambda x+(\lambda-1) y+(\lambda-4) z=7 \\ & (\lambda+1) x+(\lambda+2) y-(\lambda+2) z=9\end{aligned}\)
has infinitely many solutions, then \(\lambda^2+\lambda\) is equal to
- A \(6\)
- B \(10\)
- C \(20\)
- D \(12\)
Answer & Solution
Correct Answer
(D) \(12\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (\lambda-1) x+(\lambda-4) y+\lambda z=5 \\ & \lambda x+(\lambda-1) y+(\lambda-4) z=7 \\ & (\lambda+1) x+(\lambda+2) y-(\lambda+2) z=9 \end{aligned}\) For infinitely many solutions…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the extremities of the base of an isosceles triangle are the points \((2a,0)\) and \((0,a)\) and the equation of one of the sides is \(x = 2a\), then the area of the triangle isJEE Mains 2013 Hard
- lf \(f(x)\) is a differentiable function in the interval \((0,\infty )\) such that \(f(1) = 1\) and \(\mathop {\lim }\limits_{t \to x} \frac{{{t^2}f(x) - {x^2}f(t)}}{{t - x}} = 1,\) for each \(x > 0,\) then \(f (\frac {3}{2})\) is equal toJEE Mains 2016 Hard
- Let \(O\) be the origin, \(\vec{OP} = \vec{a}\) and \(\vec{OQ} = \vec{b}\). If \(R\) is the point on \(\vec{OP}\) such that \(\vec{OP} = 5\vec{OR}\), and \(M\) is the point such that \(\vec{OQ} = 5\vec{RM}\), then \(\vec{PM}\) is equal to :JEE Mains 2026 Easy
- If the vector \(\vec b = 3\hat j + 4\hat k\) is written as the sum of a vector \({\vec {b_1}}\) , parallel to \(\vec a = \hat i + \hat j\) and a vector \({\vec {b_2}}\) , perpendicular to \(\vec a\) , then \({\vec {b_1}} \times {\vec {b_2}}\) is equal toJEE Mains 2017 Hard
- Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3 \quad\) and \(\quad|\vec{a} \times \vec{b}|^{2}=75\).Then \(|\vec{a}|^{2}\) is equal to \(.......\)JEE Mains 2022 Hard
- Let \(x=-1\) and \(x=2\) be the critical points of the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3+\mathrm{ax}^2+\mathrm{b} \log _{\mathrm{c}}|\mathrm{x}|+1, \mathrm{x} \neq 0\). Let \(m\) and \(M\) respectively be the absolute minimum and the absolute maximum values of \(f\) in the interval \(\left[-2,-\frac{1}{2}\right]\). Then \(|\mathrm{M}+m|\) is equal to (Take \(\log _{\mathrm{c}} 2=0.7\) ):JEE Mains 2025 Medium
More PYQs from JEE Mains
- At present, a firm is manufacturing \(2000\) items. It is estimated that the rate of change of production \(P\) w.r.t. additional number of workers \(x\) is given by \(\frac{{dp}}{{dx}} = 100 - 12\sqrt x \) . If the firm employs \(25 \) more workers, then the new level of production of itmes isJEE Mains 2013 Hard
- \(\sum \limits_{ k =0}^6{ }^{51- k } C _3\) is equal toJEE Mains 2023 Medium
- If the equation, \(x^{2}+b x+45=0(b \in R)\) has conjugate complex roots and they satisfy \(|z+1|=2 \sqrt{10},\) thenJEE Mains 2020 Hard
- The maximum area of a triangle whose one vertex is at \((0,0)\) and the other two vertices lie on the curve \(y=-2 x^2+54\) at points \((x, y)\) and \((-x, y)\) where \(\mathrm{y}>0\) is :JEE Mains 2024 Hard
- The number of real values of \(\lambda \) for which the system of linear equations \(2x + 4y - \lambda z = 0\) ;\(4x + \lambda y + 2z = 0\) ; \(\lambda x + 2y+ 2z = 0\) has infinitely many solutions, isJEE Mains 2017 Hard
- The set of all values of \(a^2\) for which the line \(x + y =0\) bisects two distinct chords drawn from a point \(P\left(\frac{1+a}{2}, \frac{1-a}{2}\right)\) on the circle \(2 x ^2+2 y ^2-(1+ a ) x -(1- a ) y =0\) is equal to:JEE Mains 2023 Hard