Question
Download Solution PDFThe number of solutions of the matrix equation
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Concept:
For the two matrices to be equal, each element of first matrix must be equal to the corresponding element in the second matrix.
Calculation:
Let
So,
Then
For the two matrices to be equal, each element of first matrix must be equal to the corresponding element in the second matrix. Therefore, we get
a2 + bc =1...(i)
b(a + d) = 1...(ii)
c(a + d) = 2...(iii)
bc + d2 = 3...(iv)
From equation (i) we have
From equation (iii) and (v), we get
⇒ (1 - a2)(a + d) = 2b
⇒ a + d - a3 - a2d = 2b
⇒ a3 + a2d - a + (2b - d) = 0 is an equation of third degree and it will have three solutions.
Last updated on May 26, 2025
-> AAI ATC exam date 2025 will be notified soon.
-> 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 4th April 2025, along with the details of application dates, eligibility, and selection process.
-> 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 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.