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If A is an 3x4 matrix and B is a matrix such that A'B and BA' both are defined, then size of B is
- a)3x4
- b)3x3
- c)4x4
- d)4x3
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If A is an 3x4 matrix and B is a matrix such that AB and BA both are d...
Explanation:
Given that A is a 3x4 matrix, it means that A has 3 rows and 4 columns. Let's denote the dimensions of matrix B as m x n, where m represents the number of rows and n represents the number of columns.
To determine the size of matrix B, we need to consider the conditions for the product AB and BA to be defined.
Condition 1: AB is defined
For the product AB to be defined, the number of columns in matrix A must be equal to the number of rows in matrix B. In this case, matrix A has 4 columns, so the number of rows in matrix B must be 4.
Condition 2: BA is defined
For the product BA to be defined, the number of columns in matrix B must be equal to the number of rows in matrix A. In this case, matrix A has 3 rows, so the number of columns in matrix B must be 3.
Determining the size of matrix B
From the conditions above, we can conclude that matrix B should have 4 rows and 3 columns in order for both AB and BA to be defined.
Therefore, the size of matrix B is 4x3, which corresponds to option 'A'.
Given that A is a 3x4 matrix, it means that A has 3 rows and 4 columns. Let's denote the dimensions of matrix B as m x n, where m represents the number of rows and n represents the number of columns.
To determine the size of matrix B, we need to consider the conditions for the product AB and BA to be defined.
Condition 1: AB is defined
For the product AB to be defined, the number of columns in matrix A must be equal to the number of rows in matrix B. In this case, matrix A has 4 columns, so the number of rows in matrix B must be 4.
Condition 2: BA is defined
For the product BA to be defined, the number of columns in matrix B must be equal to the number of rows in matrix A. In this case, matrix A has 3 rows, so the number of columns in matrix B must be 3.
Determining the size of matrix B
From the conditions above, we can conclude that matrix B should have 4 rows and 3 columns in order for both AB and BA to be defined.
Therefore, the size of matrix B is 4x3, which corresponds to option 'A'.
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If A is an 3x4 matrix and B is a matrix such that AB and BA both are defined, then size of B isa)3x4b)3x3c)4x4d)4x3Correct answer is option 'A'. Can you explain this answer?
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If A is an 3x4 matrix and B is a matrix such that AB and BA both are defined, then size of B isa)3x4b)3x3c)4x4d)4x3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A is an 3x4 matrix and B is a matrix such that AB and BA both are defined, then size of B isa)3x4b)3x3c)4x4d)4x3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A is an 3x4 matrix and B is a matrix such that AB and BA both are defined, then size of B isa)3x4b)3x3c)4x4d)4x3Correct answer is option 'A'. Can you explain this answer?.
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