JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the matrices \(A=\left[\begin{array}{ccc}{1} & {1} & {2} \\ {1} & {3} & {4} \\ {1} & {-1} & {3}\end{array}\right], B=\operatorname{adj} A\) and \(\mathrm{C}=3 \mathrm{A},\) then \(\frac{|\mathrm{adjB}|}{|\mathrm{C}|}\) is equal to
- A \(72\)
- B \(2\)
- C \(8\)
- D \(16\)
Answer & Solution
Correct Answer
(C) \(8\)
Step-by-step Solution
Detailed explanation
\(A=\left[\begin{array}{rrr}{1} & {1} & {2} \\ {1} & {3} & {4} \\ {1} & {-1} & {3}\end{array}\right]\) \(\Rightarrow|A|=6\) \(\frac{|\operatorname{adj} B|}{|c|}=\frac{|\operatorname{adj}(\operatorname{adj} A)|}{|9 A|}=\frac{|A|^{4}}{3^{3}|A|}=\frac{|A|^{3}}{3^{3}}\)…
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
- Let \(\lambda \in Z, \vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}\) and \(\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}\). Let \(\overrightarrow{ c }\) be a vector such that \((\vec{a}+\vec{b}+\vec{c}) \times \vec{c}=\overrightarrow{0}, \vec{a} \cdot \vec{c}=-17\) and \(\vec{b} \cdot \vec{c}=-20\) Then \(|\overrightarrow{ c } \times(\lambda \hat{i}+\hat{j}+\hat{ k })|^2\) is equal toJEE Mains 2023 Hard
- Let for \(i\, = 1, 2, 3, p_i(x)\) be a polynomial of degree \(2\) in \(x, p'_i(x)\) and \(p"_i(x)\) be the first and second order derivatives of \(p_i(x)\) respectively. Let, \(A\left( x \right)=\left[ \begin{matrix}
{{p}_{1}}\left( x \right) & p_{1}^{'}\left( x \right) & p_{1}^{''}\left( x \right) \\
{{p}_{2}}\left( x \right) & p_{2}^{'}\left( x \right) & p_{2}^{''}\left( x \right) \\
{{p}_{3}}\left( x \right) & p_{3}^{'}\left( x \right) & p_{3}^{''}\left( x \right) \\
\end{matrix} \right]\) and \(B(x)\,= [A(x)]^T\) \(A(x)\). Then determinant of \(B(x)\)JEE Mains 2014 Hard - A complex number z is said to be unimodular if \(\left| z \right| = 1\) . Suppose \(z_1\) and \(z_2\) are complex number such that \(\frac{{{z_1} - 2{z_2}}}{{2 - {z_1}\overline {{z_2}} }}\) is unimodular and \(z_2\) is not unimodular . Then the point \(z_1\) lies on a:JEE Mains 2015 Hard
- The area of the region \(\left\{(x, y): x^2+4 x+2 \leq y \leq|x+2|\right\}\) is equal toJEE Mains 2025 Hard
- Let \(\alpha = 3+4+8+9+13+14+\ldots\) upto 40 terms. If \((\tan\beta)^{\frac{\alpha}{1020}}\) is a root of the equation \(x^2+x-2=0\), \(\beta \in \left(0, \dfrac{\pi}{2}\right)\), then \(\sin^2\beta + 3\cos^2\beta\) is equal to:JEE Mains 2026 Medium
- Let the line L pass through the point (-3, 5, 2) and make equal angles with the positive coordinate axes. If the distance of L from the point \( (-2,r,1) \) is \( \sqrt{\frac{14}{3}} \). then the sum of all possible values of r is :JEE Mains 2026 Hard
More PYQs from JEE Mains
- The total number of \(3\)-digit numbers, whose greatest common divisor with \(36\) is \(2\) , isJEE Mains 2022 Hard
- If the image of the point \(P\left( {1, - 2,3} \right)\) in the plane , \(2x + 3y - 4z + 22 = 0\) measured parallel to line , \(\frac{x}{1} = \frac{y}{4} = \frac{z}{5}\) is \(Q\) , then \(PQ \) is equal to :JEE Mains 2017 Hard
- Let \(\mathrm{n}\) denote the number of solutions of the equation \(z^{2}+3 \bar{z}=0\), where \(\mathrm{z}\) is a complex number. Then the value of \(\sum_{k=0}^{\infty} \frac{1}{n^{k}}\) is equal to:JEE Mains 2021 Hard
- If the domain of the function \( f(x)=\cos^{-1}(\frac{2x-5}{11-3x})+\sin^{-1}(2x^{2}-3x+1) \) is the interval \( [\alpha,\beta] \), then \( \alpha+2\beta \) is equal to:JEE Mains 2026 Easy
- Let \(A=\left[a_{i j}\right]\) be a square matrix of order 2 with entries either 0 or 1 . Let \(E\) be the event that \(A\) is an invertible matrix. Then the probability \(\mathrm{P}(\mathrm{E})\) is :JEE Mains 2025 Easy
- Let \(a, b\) and \(c\) be the \(7^{th},\,11^{th}\) and \(13^{th}\) terms respectively of a non -constant \(A.P.\) If these are also the three consecutive terms of a \(G.P.\) then \(\frac {a}{c}\) is equal toJEE Mains 2019 Hard