1 John 1:3 That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ.
- Luke is not a ju, he is a Greek so he's writing to his fellow non-istrealites about Jesus Christ
1 Corinthians 14:37 If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord.
- Matthew is an Apostle of which Apostles are Witness to Christ, although he was not there with Jesus Christ but he heard the story from Peter, John and James
2 Peter 1:17-18 For he received from God the Father honour and glory, when there came such a voice to him from the excellent glory, This is my beloved Son, in whom I am well pleased.
And this voice which came from heaven we heard, when we were with him in the holy mount.
- Even if they were not not eye witness, as an Apostle, they must investigate from those that are witness. That is how they write gospel of the Lord Jesus Christ