The correct option is(C): 3-Hydroxy-4 -methylpentanoic acid
The given compound is a carboxylic acid with a hydroxy group and a methyl group attached to its carbon chain. To determine its IUPAC name, let's break down the structure and identify the substituents:
Putting it all together, the IUPAC name of the compound is "3-Hydroxy-4-methylpentanoic acid."
Justification:
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to: