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The preterite and past participle forms of irregular verbs follow certain patterns. These include ending in -t (e.g. build, bend, send), stem changes (whether it is a vowel, such as in sit, win or hold, or a consonant, such as in teach and seek, that changes), or adding the [n] suffix to the past participle form (e.g. drive, show, rise ...
The past participle forms the perfect aspect with the auxiliary verb have: The chicken has eaten. 5. The past participle is used to form passive voice: The chicken was eaten. Such passive participles can appear in an adjectival phrase: The chicken eaten by the children was contaminated. Adverbially:
The present active participle is declined as a 3rd declension adjective. The ablative singular is -e , but the plural follows the i-stem declension with genitive -ium and neuter plural -ia . The perfect passive participle is declined like a 1st and 2nd declension adjective .
Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit.
This example uses peasant multiplication to multiply 11 by 3 to arrive at a result of 33. Decimal: Binary: 11 3 1011 11 5 6 101 110 2 12 10 1100 1 24 1 11000 —— —————— 33 100001 Describing the steps explicitly: 11 and 3 are written at the top
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
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