JEE Advanced · Mathematics · 18. Matrices
If the adjoint of a \(3 \times 3\) matrix \(P\) is \(\left[\begin{array}{lll}1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3\end{array}\right]\), then the possible value(s) of the determinant of \(P\) is (are)
- A \(-2\)
- B \(-1\)
- C 1
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
We know for a third order matrix \(P\),
\(|\operatorname{Adj} P|=|P|^{2}\)
Where
\(\begin{aligned}
&|\operatorname{Adj} P|=1(3-7)-4(6-7)+4(2-1)=4 \\
\therefore \quad &|P|^{2}=4 \mathrm{P}|P|=2 \text { or }-2
\end{aligned}\)
\(|\operatorname{Adj} P|=|P|^{2}\)
Where
\(\begin{aligned}
&|\operatorname{Adj} P|=1(3-7)-4(6-7)+4(2-1)=4 \\
\therefore \quad &|P|^{2}=4 \mathrm{P}|P|=2 \text { or }-2
\end{aligned}\)
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 Mathematics
- A computer producing factory has only two plants and . Plant produces and plant produces of the total computers produced. of computers produced in the factory turn out to be defective. It is known that, (computer turns out to be defective given that it is produced in plant ) (computer turns out to be defective given that it is produced in plant ). Where, denotes the probability of an event A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant isJEE Advanced 2016 Medium
- Let be the image of the point with respect to the plane Then the equation of the plane passing through and containing the straight line isJEE Advanced 2016 Medium
- The value of
\(6+\log _{\frac{3}{2}}\)\(\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}}} \cdots}}\right)\) isJEE Advanced 2012 Medium - Let be the vertices of a regular octagon that lie on a circle of radius . Let be a point on the circle and let denote the distance between the points and for . If varies over the circle, then the maximum value of the product , isJEE Advanced 2023 Hard
- The value of is equal toJEE Advanced 2016 Hard
- Paragraph:
Let \(p\) be an odd prime number and \(T_p\) be the following set of \(2 \times 2\) matrices
\[
T_p=\left\{A=\left[\begin{array}{ll}
a & b \\
c & a
\end{array}\right] ; a, b, c \in\{0,1,2, \ldots, p-1\}\right\}
\]Question:
The number of \(A\) in \(T_p\) such that the trace of \(A\) is not divisible by \(p\) but det \((A)\) is divisible by \(p\) is
[Note : The trace of a matrix is the sum of its diagonal entries.]JEE Advanced 2010 Medium
More PYQs from JEE Advanced
- The correct statement(s) about and is (are)
[Atomic number of Cr = 24 and Mn = 25]JEE Advanced 2015 Easy - Paragraph: Let be the circle in the – plane defined by the equation
Question : Let and be the chords of passing through the point and parallel to the – axis and the – axis, respectively. Let be the chord of passing through and having slope Let the tangents to at and meet at , the tangents to at and meet at and the tangents to at and meet at . Then, the points and lie on the curveJEE Advanced 2018 Medium - Let \(f(x)\) be differentiable on the interval \((0, \infty)\) such that \(f(1)=1\), and \(\lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1\) for each \(x>0\). Then, \(f(x)\) isJEE Advanced 2007 Medium
- Paragraph:
Let \(A\) be the set of all \(3 \times 3\) symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are 0 .Question:
The number of matrices \(A\) in \(A\) for which the system of linear equations \(A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]\) has a unique solution, isJEE Advanced 2009 Easy - The total number of compounds having at least one bridging oxo group among the molecules given below is
\(\text N _2\text O _5,\)\(\text P _4\text O _6,\)\(\text P _4\text O _8,\)\(\text H _4\text P _2\text O _5,\)\(\text H _5\text P _3\text O _{10},\) \(\text H _2\text S_2\text O _3,\text H _2\text S_2\text O _5\)JEE Advanced 2018 Medium - Consider an electric field \(\mathbf{E}=E_0 \hat{\mathbf{x}}\) where \(\bar{E}_0\) is a constant. The flux through the shaded area ( as shown in the figure) due to this field is
JEE Advanced 2011 Medium