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Question

Assertion :The inverse of the matrix $$A=\begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 7 \end{bmatrix}$$ does not exist. Reason: The matrix $$A$$ is singular


A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$$|A|=\begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 7 \end{vmatrix}=0$$
$$A$$ is a singular matrix.
Inverse exists iff matrix is non-singular.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Hence, option A.  

Mathematics

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