English
Hindi

Question

Download Solution PDF

The product of the cofactors of 3 and -2 in the matrix  is:

This question was previously asked in
AAI ATC Junior Executive 21 Feb 2023 Shift 1 Official Paper
Download PDF Attempt in App
View all AAI JE ATC Papers >
  1. 180
  2. -180
  3. -190
  4. 190

Answer (Detailed Solution Below)

Option 3 : -190
Free Tests
View all Free tests >
Free
AAI ATC JE Physics Mock Test
15 Qs. 15 Marks 15 Mins
Start Now

Detailed Solution

Download Solution PDF

Given:

Matrix 

Concept:

Use concept of cofactor of elements in matrix.

Calculation:

Cofactor of 3 is 

Cofactor of - 2 is 

Hence the product of the cofactors of 3 and -2 is (- 10) × 19 = - 190

Hence the option (3) is correct.

Download Solution PDF
Latest AAI JE ATC Updates

Last updated on Jun 19, 2025

-> The AAI ATC Exam 2025 will be conducted on July 14, 2025 for Junior Executive.. 

-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025. 

-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.

-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.

-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).

-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.

-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).

-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.

-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.

‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Minors and Cofactors Questions

Q1.The product of the cofactors of 3 and -2 in the matrix \(\begin{bmatrix}1&0&-2\\\ 3&-1&2\\\ 4&5&6\end{bmatrix}\) is:
Q2.With the numbers 2, 4, 6, 8, all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?
Q3.If \(R = \left[ {\begin{array}{*{20}{c}} 1&0&{ - 1}\\ 2&1&{ - 1}\\ 2&3&2 \end{array}} \right]\), the the top row of R-1 is
Q4.Find the cofactor matrix for the matrix \(A = \left[ {\begin{array}{*{20}{c}} { - 1}&2&3\\ { - 2}&3&5\\ 4&{ - 2}&1 \end{array}} \right]\) ?
Q5.Find the minor of element 7 in the determinant \({\rm{\Delta }} = \left| {\begin{array}{*{20}{c}} 1&4&3\\ 5&6&7\\ 8&9&2 \end{array}} \right|\).
Q6.What is the minor, M23 of \( \begin{bmatrix} 0 & 4 & 6\\ -4 & 0&-2 \\ -6& 2 & 0 \end{bmatrix}\)
Q7.Find the minor of element 7 in the determinant \({\rm{\Delta }} = \left| {\begin{array}{*{20}{c}} 1&4&3\\ 5&6&7\\ 8&9&2 \end{array}} \right|\).
Q8.Find the cofactor matrix for the matrix \(A = \left[ {\begin{array}{*{20}{c}} { - 1}&2&3\\ { - 2}&3&5\\ 4&{ - 2}&1 \end{array}} \right]\) ?
Q9.If \(R = \left[ {\begin{array}{*{20}{c}} 1&0&{ - 1}\\ 2&1&{ - 1}\\ 2&3&2 \end{array}} \right]\), the the top row of R-1 is

More Determinants Questions

Q1.If P is a skew-symmetric matrix of order 3, then what is det(P) equal to? 
Q2.If \(\rm D_n=\begin{vmatrix}n&20&30\\\ n^2&40&50\\\ n^3&60&70\end{vmatrix}\) then what is the value of \(\rm \Sigma_{n=1}^4D_n?\)
Q3.If \(\rm \omega=-\frac{1}{2}+i\frac{\sqrt3}{2}\) then what is \(\rm \begin{vmatrix}1+\omega &1+\omega^2&\omega+\omega^2\\\ 1&\omega\ & \omega^2\\\ \frac{1}{\omega}&\frac{1}{\omega^2}&1\end{vmatrix}\) equal to? 
Q4.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q5.If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0, where a, b, c ∈ R are non-zero and distinct; has non-zero solution, then
Q6.Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |AT A(adj(2A))–1 (adj(4B))(adj(AB))–1AAT | is equal to : 
Q7.If the system of equations  11x + y + λz = –5 2x + 3y + 5z = 3 8x – 19y – 39z = µ has infinitely many solutions, then λ4 – µ is equal to :
Q8.Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: 
Q9.Which one of the following options is incorrect?  For a square matrix A in the matrix equation AX = B. 
Q10.The area of the triangle (in unit2) whose vertices are A(4, 8),B(-6, 2) and C(5, 4) is: 
Suggested Test Series
View All >
AAI ATC Junior Executive 2025 Mock Test Series
201 Total Tests with 2 Free Tests
Start Free Test
Vocabulary Master for All Government Exams Mock Test
309 Total Tests with   1 Free Tests
Start Free Test

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti apk teen patti casino download teen patti joy official teen patti gold rummy teen patti