Bengali
English
Hindi

Question

Download Solution PDF

যদি এবং A + AT = I

যেখানে I 2 × 2 এর একক ম্যাট্রিক্স এবং AT হল A এর ট্রান্সপোজ, তাহলে θ এর মান কত?

  2. π

Answer (Detailed Solution Below)

Option 4 :
Free Tests
View all Free tests >
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins
Start Now

Detailed Solution

Download Solution PDF

ধারণা:

একটি ম্যাট্রিক্স ট্রান্সপোজ:

মূল ম্যাট্রিক্সের সারি এবং কলামগুলিকে অদলবদল করে যে নতুন ম্যাট্রিক্স পাওয়া যায় তাকে ম্যাট্রিক্সের ট্রান্সপোজ বলে।

এটি A′ বা AT দ্বারা চিহ্নিত করা হয়

সমান ম্যাট্রিক্স:

দুটি ম্যাট্রিক্স সমান হয় যদি তাদের একই মাত্রা বা ক্রম থাকে এবং সংশ্লিষ্ট উপাদানগুলি অভিন্ন হয়।

 

গণনা:

প্রদত্ত  এবং A + AT = I

A + AT = + = I

=

∴ 2cos 2θ = 1

cos 2θ =

2θ =

θ =

Download Solution PDF
Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Exams Tests Super Practice

More Transpose of a Matrix Questions

Q1.If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?
Q2.If (AB + B)T = BTX  then X is equal to ?
Q3.If \(A - 2I = \begin{bmatrix} -1 & -2 & 3 \\\ 2 & 1 & -1 \\\ -3 & 1 & 0 \end{bmatrix}\) then find AAT where I is the identity matrix of order 3 × 3.
Q4.A = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\), find (AB)T
Q5.A = \(\begin{bmatrix} 1& -1 &0 \\ 3& 2 & -1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 \\ 3\\ 5 \end{bmatrix}\), find (AB)T
Q6.If matrix A = \(\begin{bmatrix} 1 & -2 \\ -6 & 4 \end{bmatrix}\) and B = \(\begin{bmatrix} 2 & -1 \\ 1 & 3 \end{bmatrix}\), that A(BT) is:
Q7.যদি \(A = \left[ {\begin{array}{*{20}{c}} {\cos 2θ }&{ - \sin 2θ }\\ {\sin 2θ }&{\cos 2θ } \end{array}} \right]\) এবং A + AT = I যেখানে I 2 × 2 এর একক ম্যাট্রিক্স এবং AT হল A এর ট্রান্সপোজ, তাহলে θ এর মান কত?
Q8.যদি A, B একই ক্রমে বর্গ ম্যাট্রিক্স হয় এবং B একটি বি-প্রতিসম ম্যাট্রিক্স হয়, তাহলে A′BA হল:
Q9.If A and B are square matrices of the same order, then (AB′ - BA′) is a:

More Matrices Questions

Q1.What is A-1 equal to?  
Q2.What is A(adj A) equal to?  
Q3.Consider the following in respect of the matrices  \(\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}\) I. PQ is a null matrix.  II. QP is an identity matrix of order 3.  III. PQ = QP Which of the above is/are correct? 
Q4.Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct? 
Q5.Let X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct? I. (ZY)X is defined and is a square matrix of order 3. II. Y(XZ) is defined and is a square matrix of order 2. III. X(YZ) is not defined. Select the answer using the code given below.
Q6.If \(A=\left[\begin{array}{cc} 1 & 3 \\ 0 & -1 \end{array}\right]\), then trace of 5A5 + 4A4 + 3A3 + 2A2 + A + I2 is :
Q7.Let α be a root of the equation x2 + x+ 1= 0 and the matrix A = \(\frac{1}{\sqrt{3}}\left[\begin{array}{ccc} 1 & 1 & 1 \\ 1 & \alpha & \alpha^2 \\ 1 & \alpha^2 & \alpha^4 \end{array}\right]\) then the matrix A31 is equal to
Q8.ধরা যাক A এবং B দুটি 3 x 3 বাস্তব ম্যাট্রিক্স এমন যে A একটি প্রতিসম ম্যাট্রিক্স এবং B একটি বিপ্রতিসম ম্যাট্রিক্স। তাহলে (A2B2 − B2A2)X = O রৈখিক সমীকরণের নিয়ম, যেখানে X অজ্ঞাত চলকের 3 x 1 স্তম্ভ ম্যাট্রিক্স এবং O একটি 3 x 1 শূন্য ম্যাট্রিক্স, এর সমাধান হবে:
Q9.Let α ∈ (0, α) and \(A = \begin{bmatrix} 1 & 2 & \alpha \\\ 1 & 0 & 1 \\\ 0 & 1 & 2 \end{bmatrix}\). If det(adj(2A - AT). adj(A - 2AT)) = 28, then (det(A))2 is equal to: 
Q10.For a 3 × 3 matrix A = [aij], whose element aij is given by aij = \(\rm \sqrt{i^2+3j}\) then what is element a31?
Suggested Test Series
View All >
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with 1 Free Tests
Start Free Test
Current Affairs (CA) 2024 Mega Pack for SSC/Railways/State Exam Mock Test
427 Total Tests with   1 Free Tests
Start Free Test

NDA Important Links

ResultAdmit CardApplication FormEligibilitySalarySyllabus

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： all teen patti game teen patti gold downloadable content teen patti download teen patti real cash withdrawal