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For a square matrix A in a matrix equation AX = B, if │A│≠ 0, then
- a)There exists a unique solution
- b)There exists no solution
- c)There exists infinite number of solutions
- d)The system may or may not be consistent
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
For a square matrix A in a matrix equation AX = B, if A 0, thena)There...
Solution:
Given, AX = B, where A is a square matrix.
If A is invertible (i.e., A 0), then there exists a unique solution for X.
Explanation:
When A is invertible, it means that there exists a unique matrix A-1 such that A-1A = I, where I is the identity matrix.
Now, if we multiply both sides of the given equation by A-1, we get:
A-1AX = A-1B
⇒ IX = A-1B (using A-1A = I)
⇒ X = A-1B
Hence, we get a unique solution for X, which is X = A-1B.
This is because the inverse of a matrix is unique, and so there can be only one solution for X.
Therefore, the correct option is (A) - There exists a unique solution.
Given, AX = B, where A is a square matrix.
If A is invertible (i.e., A 0), then there exists a unique solution for X.
Explanation:
When A is invertible, it means that there exists a unique matrix A-1 such that A-1A = I, where I is the identity matrix.
Now, if we multiply both sides of the given equation by A-1, we get:
A-1AX = A-1B
⇒ IX = A-1B (using A-1A = I)
⇒ X = A-1B
Hence, we get a unique solution for X, which is X = A-1B.
This is because the inverse of a matrix is unique, and so there can be only one solution for X.
Therefore, the correct option is (A) - There exists a unique solution.
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Community Answer
For a square matrix A in a matrix equation AX = B, if A 0, thena)There...
Given, AX = B, where A is a square matrix.
If A is invertible (i.e., A 0), then there exists a unique solution for X.
Explanation: When A is invertible, it means that there exists a unique matrix A-1 such that A-1A = I, where I is the identity matrix.
Now, if we multiply both sides of the given equation by A-1, we get: A-1AX = A-1B ⇒ IX = A-1B (using A-1A = I) ⇒ X = A-1B
Hence, we get a unique solution for X, which is X = A-1B. This is because the inverse of a matrix is unique, and so there can be only one solution for X.
Therefore, the correct option is (A) - There exists a unique solution.
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For a square matrix A in a matrix equation AX = B, if A 0, thena)There exists a unique solutionb)There exists no solutionc)There exists infinite number of solutionsd)The system may or may not be consistentCorrect answer is option 'A'. Can you explain this answer?
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