= Solution
The first row has off-diagonal sum $a_{12}<1/4$. Rows $2,\ldots,n-1$ have sums less than $1/2$, and the last row has sum $c+a_{n,n-1}<5/4$, since $0<c<1$. Every row except the second therefore has its <Gershgorin disc> strictly away from zero: its centre is at least one in the first row and at least three in the remaining rows.
For the second row, an exact sufficient condition is $|b|>a_{21}+a_{23}$. Since the sum is strictly below $1/2$, the coefficient-independent bounds
$$
\boxed{b\leq-\frac12\quad\text{or}\quad b\geq\frac12}
$$
guarantee that zero is outside every <Gershgorin disc>. Consequently zero is not an <eigenvalue> and $A$ is an <invertible matrix>. Equality at $\pm1/2$ is allowed because the off-diagonal entry bounds are strict. These are sufficient <strict diagonal dominance> bounds; values of $b$ between them can also give invertible <matrices>.
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