Class 12 Exam > Class 12 Questions > If matrix A = [2 3 5], then the value of A.A ...
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If matrix A = [2 3 5], then the value of A.A' is:
- a)38
- b)26
- c)39
- d)28
Correct answer is option 'A'. Can you explain this answer?
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If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correc...
A = [2 3 5]
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If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correc...
A = [2 3 5]
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If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correc...
Understanding Matrix Multiplication
Matrix multiplication involves taking the dot product of rows and columns. In this case, we have a 1x3 matrix A = [2, 3, 5]. To find A.A, we will multiply matrix A by itself.
Calculating A.A
1. Matrix A:
A = [2, 3, 5]
2. Transpose of A:
A^T =
[
2
3
5
]
3. Multiplication:
A.A = A * A^T = [2, 3, 5] * [2, 3, 5]
4. Dot Product Calculation:
The product is calculated as follows:
- For the first element: 2*2 + 3*3 + 5*5
- Calculation:
- 2*2 = 4
- 3*3 = 9
- 5*5 = 25
5. Summing the Products:
- 4 + 9 + 25 = 38
Conclusion
Thus, the value of A.A is 38, which corresponds to option 'A'.
Final Verification
- Steps Recap:
- Identify the elements of matrix A.
- Multiply A with its transpose.
- Sum the results of the products to get the final value.
By following these steps, we confirm that the correct answer is indeed 38.
Matrix multiplication involves taking the dot product of rows and columns. In this case, we have a 1x3 matrix A = [2, 3, 5]. To find A.A, we will multiply matrix A by itself.
Calculating A.A
1. Matrix A:
A = [2, 3, 5]
2. Transpose of A:
A^T =
[
2
3
5
]
3. Multiplication:
A.A = A * A^T = [2, 3, 5] * [2, 3, 5]
4. Dot Product Calculation:
The product is calculated as follows:
- For the first element: 2*2 + 3*3 + 5*5
- Calculation:
- 2*2 = 4
- 3*3 = 9
- 5*5 = 25
5. Summing the Products:
- 4 + 9 + 25 = 38
Conclusion
Thus, the value of A.A is 38, which corresponds to option 'A'.
Final Verification
- Steps Recap:
- Identify the elements of matrix A.
- Multiply A with its transpose.
- Sum the results of the products to get the final value.
By following these steps, we confirm that the correct answer is indeed 38.
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If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correct answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correct answer is option 'A'. Can you explain this answer?.
If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correct answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If matrix A = [2 3 5], then the value of A.A is:a)38b)26c)39d)28Correct answer is option 'A'. Can you explain this answer?.
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