JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(2 x+3 y-z=-2\) ; \(x+y+z=4\) ; \(x-y+|\lambda| z=4 \lambda-4\) (where \(\lambda \in R\)), has no solution, then
- A \(\lambda=7\)
- B \(\lambda=-7\)
- C \(\lambda=8\)
- D \(\lambda^{2}=1\)
Answer & Solution
Correct Answer
(B) \(\lambda=-7\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}2 & 3 & -1 \\ 1 & 1 & 1 \\ 1 & -1 & \mid \lambda\mid\end{array}\right|=0\) \(\Rightarrow|\lambda|=7 \Rightarrow \lambda=\pm 7.......(1)\) System: \(2 x+3 y-z=-2........(2)\) \(x+y+z=4.......(3)\) \(x-y+|\lambda| z=4 \lambda-4......(4)\) Eliminating y…
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
- The number of non-empty equivalence relations on the set \(\{1,2,3\}\) is :JEE Mains 2025 Easy
- If \(y=y(x)\) is the solution of the equaiton \(e ^{\sin y} \cos y \frac{ dy }{ dx }+ e ^{\sin y} \cos x =\cos x , y (0)=0\) then \(1+ y \left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2} y \left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}} y \left(\frac{\pi}{4}\right)\) is equal toJEE Mains 2021 Hard
- Let \(f(x)=x^2+9, g(x)=\frac{x}{x-9}\) and \(\mathrm{a}=\mathrm{fog}(10), \mathrm{b}=\operatorname{gof}(3)\). If \(\mathrm{e}\) and \(1\) denote the eccentricity and the length of the latus rectum of the ellipse \(\frac{x^2}{a}+\frac{y^2}{b}=1\), then \(8 e^2+1^2\) is equal to.JEE Mains 2024 Hard
- The least positive integer \(n\) such that \(1 - \frac{2}{3} - \frac{2}{{{3^2}}} - .... - \frac{2}{{{3^{n - 1}}}} < \frac{1}{{100}},\) isJEE Mains 2014 Hard
- If the system of linear equations \(2 x+y-z=3\) \(x-y-z=\alpha\) \(3 x+3 y+\beta z=3\) has infinitely many solution, then \(\alpha+\beta-\alpha \beta\) is equal to .... .JEE Mains 2021 Medium
- The number of six letter words (with or without meaning), formed using all the letters of the word \('VOWELS',\) so that all the consonants never come together, is ... .JEE Mains 2021 Easy
More PYQs from JEE Mains
- Let \(y=y(x)\) be the solution of the differential equation \(e^{x} \sqrt{1-y^{2}} d x+\left(\frac{y}{x}\right) d y=0, y(1)=-1\) Then the value of \((y(3))^{2}\) is equal to:JEE Mains 2021 Hard
- A circle cuts a chord of length \(4a\) on the \(x -\) axis and passes through a point on the \(y -\) axis, distant \(2b\) from the origin. Then the locus of the center of this circle, isJEE Mains 2019 Hard
- Let \(f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}\). Then \(\lim _{x \rightarrow 0} \frac{f(x)}{x^3}\) is equal toJEE Mains 2024 Hard
- If for \(x \in\left(0, \frac{\pi}{2}\right), \log _{10} \sin x+\log _{10} \cos x=-1\) and \(\log _{10}(\sin x+\cos x)=\frac{1}{2}\left(\log _{10} n-1\right), n>0\) then the value of \(n\) is equal toJEE Mains 2021 Hard
- A number is called a palindrome if it reads the same backward as well as forward. For example \(285582\) is a six digit palindrome. The number of six digit palindromes, which are divisible by \(55\), is ...... .JEE Mains 2021 Hard
- The urns \(A, B\) and \(C\) contain \(4\) red, \(6\) black;\(5\) red,\(5\) black and \(\lambda\) red,\(4\) black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn \(C\) is \(0.4\) then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola \(y^2=\lambda x\) with one vertex at the vertex of the parabola isJEE Mains 2023 Hard