How many values can be held by an array A (-3:10, 5:12) ?

Concept. When an array dimension is declared with explicit lower and upper bounds written as lower:upper, BOTH bounds are inclusive. The number of elements along that dimension (its extent) is therefore

extent = upper − lower + 1.

For a multi-dimensional array, the total number of storable values is the PRODUCT of the extents of every dimension.

Application. The declaration A(−3:10, 5:12) has two dimensions:

1. First dimension runs from −3 to 10, so its extent = 10 − (−3) + 1 = 14.

2. Second dimension runs from 5 to 12, so its extent = 12 − 5 + 1 = 8.

3. Total values = 14 × 8 = 112.

Cross-check. Counting the first dimension directly — −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 — gives 14 distinct indices, and the second dimension 5, 6, 7, 8, 9, 10, 11, 12 gives 8 indices. The grid of index pairs has 14 × 8 = 112 cells, confirming the array holds 112 values.