AP EAMCET · Maths · Determinants
The values of \(\lambda\) and \(\mu\) for which the system of equations \(x+y+z=6, x+2 y+3 z=10, x+2 y+\lambda z=\mu\) has infinitely many solutions are
- A \(\lambda=3, \mu=7\)
- B \(\lambda \neq 3, \mu=10\)
- C \(\lambda=3, \mu=10\)
- D \(\lambda=3, \mu \neq 10\)
Answer & Solution
Correct Answer
(C) \(\lambda=3, \mu=10\)
Step-by-step Solution
Detailed explanation
\(\begin{pmatrix} 1 & 1 & 1 & | & 6 \\ 1 & 2 & 3 & | & 10 \\ 1 & 2 & \lambda & | & \mu \end{pmatrix}\) \(R_2 \leftarrow R_2-R_1, R_3 \leftarrow R_3-R_1\) \(\begin{pmatrix} 1 & 1 & 1 & | & 6 \\ 0 & 1 & 2 & | & 4 \\ 0 & 1 & \lambda-1 & | & \mu-6 \end{pmatrix}\)…
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 \(y=(1+x)\left(1+x^2\right)\left(1+x^4\right) \ldots\left(1+x^{2 n}\right)\), then \(\left(\frac{d y}{d x}\right)_{x=0}\) is equal toAP EAMCET 2011 Medium
- The area (in sq. units) of the region bounded by the lines \(x=0, x=\frac{\pi}{2}\) and \(f(x)=\sin x, g(x)=\cos x\) isAP EAMCET 2025 Medium
- The transformed equation of \(2 x^2+3 y^2-z^2-8 x+18 y\) \(+2 z+9=0\) when the axes are translated to the point \((2,-3,1)\) isAP EAMCET 2023 Easy
- If the eccentric angles of the extremeties of a focal chord (other than the major axis) of the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) are \(\alpha\) and \(\beta\) then \(\frac{\cot \left(\frac{\alpha}{2}\right)}{\tan \left(\frac{\beta}{2}\right)}=\)AP EAMCET 2017 Medium
- \(\cos ^3 110^{\circ}+\cos ^3 10^{\circ}+\cos ^3 130^{\circ}=\)AP EAMCET 2018 Easy
- If \(R\) is the set of all real numbers and \(f: R-\{2\} \rightarrow R\) is defined by \(f(x)=\frac{2+x}{2-x}\) for \(x \in R-\{2\}\)AP EAMCET 2014 Medium
More PYQs from AP EAMCET
- The angle between the lines represented by isAP EAMCET 2021 Medium
- The orthocentre of the triangle formed by lines \(x+y+1=0 ; x-y-1=0\) and \(3 x+4 y+5=0\) isAP EAMCET 2024 Easy
- Methane of the polluted air reacts with ozone and forms the compounds.AP EAMCET 2018 Medium
- The correct statement about the product of the following reaction is
\(\mathrm{CH}_3 \mathrm{CHO} \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O}]{\text { (i) } \mathrm{C}_2 \mathrm{H}_5 \mathrm{MgBr}}\) productAP EAMCET 2025 Medium - If a chord of the parabola \(y^2=4 x\) passes through its focus and makes an angle \(\theta\) with the \(X\)-axis, then its length isAP EAMCET 2011 Hard
- If , where . Then findAP EAMCET 2021 Medium