"I write in the book."
Translation:In libro scribo.
There are many ways to talk about a place in Latin. When, like in this sentence, the latin preposition "in" is used, we can use one of two cases: accusative or ablative.
We use accusative when there is movement toward someplace involved: "When Caesar arrived in Gaul..." => "Cum Caesar in GalliAM venit..." (Gallic War 6,12,1)
We use ablative when the action takes place in a place without movement involved: "There was only one legion in [...] Gaul." => "Erat in GalliA [...] legio una." (Gallic War 1,7,2)
In this exercise, there is no movement, so we use the ablative case "in libro".
Since it is a lesson about accusative, maybe it would be less confusing for the post-beta Latin course to move this type of sentences a few lessons further.
For some languages it is a movement, like in German it is followed by the Accusative, or in Czech you use a moving preposition. Since no Romanic language seem to consider it a motion today, the ablative might be the most apropriate. My Latin Ego also tends to in librum, but in+Acc is usually followed by commentaries (e.g. In IV libros sententiarum, rather "about". Plus I am a barbarus germanus, my sense might be simply wrong.
Actually, the case is defined by the preposition. It could be either accusative: "in librUM", indicating a movement = "into the book"; or it could be ablative, without movement: "in librO" = "in the book". Duo thinks of it as being without movement. I am not sure I agree, since something happens from the pen to the paper.
Every time the word order is different (if there are no word groups as "in urbe"), and every time there is a personal pronoun, they are all okay with different word order, and with or without the personal prononouns subject, and since they are all okay, and we know it, we shouldn't write here, but report with the "report" button.
All those are okay, and if there are no accepted yet, please report, and let's wait (it takes times):
Ego in libro scribo, In libro scribo, Scribo in libro, Ego scribo in libro, etc...
It can't be in the nominative. It takes its case from the preposition "in", which here refers to a static location, so it must be ablative.
The accusative is for direct objects. That means the thing which is "verbed". The accusative case answers the question "who/what was verbed?" I'm using "verb" here as a stand-in variable for any verb. In this case, the verb is "write". If we answer the question, "what did I write," the answer is not going to be "in the book", unless "in the book" is literally the actual phrase that you physically wrote. But, of course, that's not the sentence being used in the question here. In the actual sentence here, the phrase "in the book" (in libro) answers the question, "where did I write," or, more specifically, "what did I write on?" It does not answer the question, "what did I write?" If we had a sentence like, "I wrote the answer in the book", then "the answer" might be in the accusative, because that's what we wrote. I say "might" because I don't know for sure if that's how Latin would handle it, but that's how the accusative works in a generalized sense, at least. That's the distinction that the accusative makes, and that's why we can't use the accusative here. And, so far as I understand it, Latin uses the ablative for locations that don't otherwise take the locative case, so the ablative "libro" is used.
I'm not sure what you're asking here. Latin nouns (and adjectives) come in 3 grammatical genders (masculine, feminine, and neuter) and 5 declension patterns. [1, 2, 3] [4, 5] Which case a noun is in depends on its role in the sentence. If it is the subject or the subject complement, it will be in nominative form. Here, however, it is in ablative form.
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.