COMEDK · Maths · 21. Matrices
If the matrix \(M = \begin{bmatrix} x+5 & a & -4 \\ -2 & 0 & b \\ c & 6 & y+1 \end{bmatrix}\) is a skew symmetric matrix, the value of the expression \(ab + c^2 - xy\) is:
- A \(0\)
- B \(-9\)
- C \(-1\)
- D \(-33\)
Answer & Solution
Correct Answer
(C) \(-1\)
Step-by-step Solution
Detailed explanation
For a skew-symmetric matrix \(M\), \(M^T = -M\). The diagonal elements must be zero: \(x + 5 = 0 \Rightarrow x = -5\) \(y + 1 = 0 \Rightarrow y = -1\) For non-diagonal elements, \(m_{ij} = -m_{ji}\): \(m_{12} = -m_{21} \Rightarrow a = -(-2) = 2\)…
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 \(\log _{10} 7=0.8451\), then the position of the first significant figure of \(7^{-20}\) isCOMEDK 2019 Medium
- Middle term of the expansion \(\left(x^2+\frac{1}{x^2}+2\right)^n\) isCOMEDK 2024 Easy
- The equation of a circle passing through the origin is \(x^2+y^2-6 x+2 y=0\). The equation of one of its diameter isCOMEDK 2024 Easy
- A bag contans white balls and red balls. balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then is equal toCOMEDK 2022 Medium
- In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failure will beCOMEDK 2023 Medium
- If \(e_{1}\) and \(e_{2}\) are the eccentricities of a hyperbola \(3 x^{2}-3 y^{2}=25\) and its conjugate, thenCOMEDK 2019 Medium
More PYQs from COMEDK
- Find the co-ordinates of the orthocentre of the triangle formed by the lines
\(L_1: y - x = 2\)
\(L_2: y + 2x = 8\)
\(L_3: 3y - x = 18\)COMEDK 2026 Medium - The point \((5,-7)\) lies outside the circleCOMEDK 2018 Easy
- The resistance of the conductor is \(\sqrt{3} \Omega\) the angle made by the V-I graph with the voltage axis is \(\theta\)COMEDK 2025 Medium
- The value of \(\cos \left(\frac{\pi}{4}-x\right) \cos \left(\frac{\pi}{4}-y\right)\)
\(-\sin \left(\frac{\pi}{4}-x\right) \sin \left(\frac{\pi}{4}-y\right)\) is equal toCOMEDK 2017 Easy - \(\text { A square matrix } P \text { satisfies } P^2=I-P \text { where } I \text { is identity matrix. If } P^n=5 I-8 P \text {, then } n \text { is equal to }\)COMEDK 2024 Medium
- The resistance of a wire is 5 ohm at \(25^{\circ} \mathrm{C}\) and 7 ohm at \(100^{\circ} \mathrm{C}\). The resistance of the wire at \(0^{\circ} \mathrm{C}\) isCOMEDK 2025 Medium