<p>Linear descriptor systems are widely used to model dynamic processes in engineering, economics and biological systems. Unlike normal systems, descriptor systems can capture both dynamic and algebraic constraints, making them suitable for complex real-world applications. However, their structural properties, such as observability and detectability, are more challenging to analyse due to their implicit nature. Existing methods for checking these properties often rely on restrictive assumptions or are limited to square systems. Moreover, the algebraic criteria used are not as easy to apply as normal systems. Therefore, it is imperative to devise effective techniques for checking the observability and detectability of descriptor systems based on normal systems. A new approach is proposed to check the observability and the detectability for rectangular linear descriptor systems. Under the assumption of impulse observability, we prove that strong observability and detectability are equivalent to the observability and detectability of a normal system. The essence of the technique for designing the proposed normal system is based on an equivalent form for descriptor systems. This paper derives effective algebraic criteria and necessary and sufficient conditions for checking the observability and detectability of descriptor systems based on a suitably designed natural system. For illustration, some real-world problems are presented.</p>