Explanation:

- The Brihadeshwara Temple at Tanjore is a magnificent example of Dravidian architecture.

- Option 1: Rajaraja I

- He was a renowned Chola ruler.

- Constructed the Brihadeshwara Temple around 1010 AD.

- Known for expanding the Chola empire and his patronage to the arts.

- Option 2: Rajendra I

- Son of Rajaraja I.

- Succeeded him and carried forward his legacy, building other temples.

- Option 3: Vijayalaya

- Founder of the Chola Empire.

- Not associated with the construction of Brihadeshwara Temple.

- Option 4: Rajendra III

- Last ruler of the Chola dynasty.

- Ruled much later than the construction of the Brihadeshwara Temple.