this section has four choices (a), (b), (c) and (d) out of which only one is correct. Mark your choices as follows:
(a) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
(b) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
(c) STATEMENT-1 is True, STATEMENT-2 is False
(d) STATEMENT-1 is False, STATEMENT-2 is True
- Statement-1: As \( A=\left[\begin{array}{lll}2 & 1 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 2\end{array}\right] \) satisfies the equation \( x^{3}-5 x^{2}+7 x-3=0 \), therefore \( A \) is invertible.
Statement-2: If a square matrix \( A \) satisfies the equation \( a_{0} x^{n}+a_{1} x^{n-1}+\ldots a_{n-1} x+a_{n}=0 \), and \( a_{n} \neq 0 \), then \( A \) is invertible.
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