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If A and B are two matrices such that A + B and AB are both defined, then
- a)A and B can be any matrices
- b)A, B are square matrices not necessarily of same order
- c)A, B are square matrices of same order
- d)number of columns of A = number of rows of B
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If A and B are two matrices such that A + B and AB are both defined, t...
Since A+B is defined, A and B are matrices of the same type,
say m×n; Also, AB is defined.
So, the number of columns in A must be equal to the number of rowsin B ie. n=m.
Hence, A and B are square matrices of the same order.
say m×n; Also, AB is defined.
So, the number of columns in A must be equal to the number of rowsin B ie. n=m.
Hence, A and B are square matrices of the same order.
Most Upvoted Answer
If A and B are two matrices such that A + B and AB are both defined, t...
If you want to add two matrices then thier order must be same. also if you want the product of two matrices then the matrices have to be square matrices. Thus Correct ans. is 3.
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If A and B are two matrices such that A + B and AB are both defined, t...
Explanation:
Let's break down the information given in the question and analyze each option to determine the correct answer.
Given information:
- A and B are two matrices.
- AB is defined, which means the product of A and B exists.
- BA is defined, which means the product of B and A exists.
Analysis of options:
a) A and B can be any matrices
- This option suggests that A and B can be any type of matrices, regardless of their dimensions or properties. However, this is not necessarily true because the products AB and BA must be defined. So, this option is incorrect.
b) A, B are square matrices not necessarily of the same order
- This option states that both A and B are square matrices, meaning they have an equal number of rows and columns. However, it does not require them to have the same dimensions. This option is also incorrect because the products AB and BA must be defined, which requires the dimensions of A and B to be compatible.
c) A, B are square matrices of the same order
- This option suggests that both A and B are square matrices and have the same dimensions. If A and B are square matrices, then the products AB and BA can be defined as long as they have the same dimensions. Therefore, this option is correct.
d) The number of columns of A is equal to the number of rows of B
- This option states that the number of columns of A must be equal to the number of rows of B. This condition ensures that the matrix multiplication is possible. Therefore, this option is correct.
Conclusion:
Based on the analysis of the given information and options, the correct answer is option 'C': A, B are square matrices of the same order. This is because both A and B need to be square matrices with the same dimensions for the products AB and BA to be defined. Additionally, option 'D' is also correct because the number of columns of A must be equal to the number of rows of B for matrix multiplication to be possible.
Let's break down the information given in the question and analyze each option to determine the correct answer.
Given information:
- A and B are two matrices.
- AB is defined, which means the product of A and B exists.
- BA is defined, which means the product of B and A exists.
Analysis of options:
a) A and B can be any matrices
- This option suggests that A and B can be any type of matrices, regardless of their dimensions or properties. However, this is not necessarily true because the products AB and BA must be defined. So, this option is incorrect.
b) A, B are square matrices not necessarily of the same order
- This option states that both A and B are square matrices, meaning they have an equal number of rows and columns. However, it does not require them to have the same dimensions. This option is also incorrect because the products AB and BA must be defined, which requires the dimensions of A and B to be compatible.
c) A, B are square matrices of the same order
- This option suggests that both A and B are square matrices and have the same dimensions. If A and B are square matrices, then the products AB and BA can be defined as long as they have the same dimensions. Therefore, this option is correct.
d) The number of columns of A is equal to the number of rows of B
- This option states that the number of columns of A must be equal to the number of rows of B. This condition ensures that the matrix multiplication is possible. Therefore, this option is correct.
Conclusion:
Based on the analysis of the given information and options, the correct answer is option 'C': A, B are square matrices of the same order. This is because both A and B need to be square matrices with the same dimensions for the products AB and BA to be defined. Additionally, option 'D' is also correct because the number of columns of A must be equal to the number of rows of B for matrix multiplication to be possible.
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If A and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer?
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If A and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. 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 and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. 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 and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer?.
If A and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. 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 and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. 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 and B are two matrices such that A + B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of same orderc)A, B are square matrices of same orderd)number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer?.
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