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

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 AssertionHence, option A.   Mathematics

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