Matjurtagarðurinn er tilbúinn.

It is a compound noun:

• matjurta- = vegetable(s)
• garður = garden
• -inn = the attached to the end

So matjurtagarðurinn means the vegetable garden.

A very literal breakdown would be something like the garden of vegetables.

That -a- is part of how the compound is formed. In Icelandic, the first part of a compound often appears in a linking form, very often related to a genitive form.

Here:

• base word: matjurt = vegetable / edible plant
• compound form: matjurta-

So matjurtagarður is not just matjurt + garður mechanically stuck together; it uses the normal compound form matjurta-.

This is very common in Icelandic compounds, and it is something learners often just get used to over time.

Icelandic usually puts the definite article on the end of the noun.

So:

• matjurtagarður = a vegetable garden
• matjurtagarðurinn = the vegetable garden

That ending changes depending on gender, number, and case. Here -inn is the masculine singular nominative definite ending.

Icelandic does have a separate article word hinn, but in ordinary sentences the suffixed article is the normal choice.

Er is the present-tense singular form of vera, which means to be.

So:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

Since matjurtagarðurinn is singular, Icelandic uses er:

• Matjurtagarðurinn er tilbúinn.
• The vegetable garden is ready.

Because Icelandic adjectives agree with the noun they describe in gender, number, and case.

Here, the subject matjurtagarðurinn is:

• masculine
• singular
• nominative

So the adjective also appears in the masculine singular nominative form:

• tilbúinn

Compare:

• masculine: tilbúinn
• feminine: tilbúin
• neuter: tilbúið

So if the noun were feminine or neuter, the adjective would change.

Because this adjective is being used predicatively after er.

In Icelandic, that matters a lot.

• Predicative adjective: Garðurinn er tilbúinn. = The garden is ready.
• Attributive adjective: tilbúni garðurinn = the ready garden

When the adjective comes after to be and describes the subject, Icelandic normally uses the regular agreeing form, not the weak definite form you often see before a definite noun.

So:

• Matjurtagarðurinn er tilbúinn. is correct.
• tilbúni matjurtagarðurinn would be a different structure: the ready vegetable garden.

In Icelandic compounds, the last part usually determines the gender of the whole word.

The final part here is:

• garður = garden

And garður is a masculine noun.

So the whole compound matjurtagarður is also masculine, and that affects:

• the definite ending: -inn
• the adjective form: tilbúinn

This is a very useful rule for compounds in Icelandic.

Yes. This is the most neutral, standard order:

• Matjurtagarðurinn = subject
• er = verb
• tilbúinn = subject complement / predicate adjective

So it is simply:

• Subject + verb + complement

If you wanted to turn it into a yes/no question, you would usually move the verb first:

• Er matjurtagarðurinn tilbúinn?
• Is the vegetable garden ready?

A rough English-friendly guide is:

• Matjurtagarðurinn ≈ MAHT-yur-ta-gar-thur-inn
• er ≈ ehr
• tilbúinn ≈ til-BOO-inn

A few useful sound notes:

• j sounds like English y
• ð sounds like th in this
• ú sounds like oo in food
• stress usually falls on the first syllable of each word

So the rhythm is roughly:

MAHT-yur-ta-gar-thur-inn ehr til-BOO-inn