UPSC Exam > UPSC Questions > If A and B are square matrices of order 3×3 a...
Start Learning for Free
If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than?
Most Upvoted Answer
If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the...
Explanation:
- The determinant of a matrix is a scalar value that can be computed from the elements of a square matrix and is denoted by |A|.
- The adjugate of a matrix A, denoted as adj(A), is the transpose of the cofactor matrix of A.
- Let's calculate |(adj(adj(adj(AB)))| step by step:
Step 1: Calculate the matrix AB
- Since A and B are 3x3 matrices, the product AB will also be a 3x3 matrix.
Step 2: Calculate the determinant of AB
- |AB| = |A| * |B| = 2 * 1 = 2
Step 3: Calculate the adjugate of AB
- adj(AB) is the transpose of the cofactor matrix of AB.
Step 4: Calculate the adjugate of adj(AB)
- adj(adj(AB)) is the transpose of the cofactor matrix of adj(AB).
Step 5: Calculate the adjugate of adj(adj(AB))
- adj(adj(adj(AB))) is the transpose of the cofactor matrix of adj(adj(AB)).
- The value of |(adj(adj(adj(AB)))| will be the determinant of the matrix obtained in Step 5.
- Since the determinant of a matrix is a scalar value, it will always be less than 2 (|A| = 2).
Therefore, the value of |(adj(adj(adj(AB)))| is always less than 2.
- The determinant of a matrix is a scalar value that can be computed from the elements of a square matrix and is denoted by |A|.
- The adjugate of a matrix A, denoted as adj(A), is the transpose of the cofactor matrix of A.
- Let's calculate |(adj(adj(adj(AB)))| step by step:
Step 1: Calculate the matrix AB
- Since A and B are 3x3 matrices, the product AB will also be a 3x3 matrix.
Step 2: Calculate the determinant of AB
- |AB| = |A| * |B| = 2 * 1 = 2
Step 3: Calculate the adjugate of AB
- adj(AB) is the transpose of the cofactor matrix of AB.
Step 4: Calculate the adjugate of adj(AB)
- adj(adj(AB)) is the transpose of the cofactor matrix of adj(AB).
Step 5: Calculate the adjugate of adj(adj(AB))
- adj(adj(adj(AB))) is the transpose of the cofactor matrix of adj(adj(AB)).
- The value of |(adj(adj(adj(AB)))| will be the determinant of the matrix obtained in Step 5.
- Since the determinant of a matrix is a scalar value, it will always be less than 2 (|A| = 2).
Therefore, the value of |(adj(adj(adj(AB)))| is always less than 2.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than?
Question Description
If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than?.
If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than?.
Solutions for If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? defined & explained in the simplest way possible. Besides giving the explanation of
If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than?, a detailed solution for If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? has been provided alongside types of If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? theory, EduRev gives you an
ample number of questions to practice If A and B are square matrices of order 3×3 and|A| =2, |B|=1, then the value of |(adj(adj(adj(AB)))| is always less than? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup