Question
Download Solution PDFमाना \(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) और \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\), जैसे कि A2 = B, तो α का मान है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) और \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\) जैसे कि A2 = B
संकल्पना:
दो आव्यूह तब समान होते हैं जब दोनों आव्यूहों के लिए सभी स्थितीय अवयव समान होते हैं।
गणना:
\(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) और \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)
तब
\(A^2=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\cdot \left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\)
\(A^2=\left(\begin{array}{cc} α^2 & α-1 \\ 0 & 1 \end{array}\right)\)
दिया गया है A2 = B तब
\(\left(\begin{array}{cc} α^2 & α-1 \\ 0 & 1 \end{array}\right)=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\)
⇒ α2 = 4 और α - 1 = 1
⇒ α = ± 2 और α = 2
तब α = 2
अतः विकल्प (3) सही है।
Last updated on Jul 4, 2025
-> AAI Junior Executive city intimation slip 2025 has been released at the official website.
-> 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.