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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?
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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.
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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?
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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?.
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