The system of three linear equations in three unknown variables can be written in the matrix form…
Assertion: The system of three linear equations in three unknown variables can be written in the matrix form as $AX = B$. It has a unique solution $X = A^{-1}B$.
Reason: Matrix $A$ is non-singular.
- aBoth Assertion and Reason are true and Reason is the correct explanation for Assertion.
- bBoth Assertion and Reason are true but Reason is not the correct explanation for Assertion.
- cAssertion is true and Reason is false.
- dAssertion is false and Reason is true.
Answer
Answer
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Correct option: a
A system of three linear equations $AX = B$ has a unique solution $X = A^{-1}B$ if and only if the matrix $A$ is non-singular ($|A| \ne 0$), in which case $A^{-1}$ exists. Thus both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
From ISC 2026 Mathematics Paper 1, question 1(xi).