You don't want transaction data in the member table.
The transaction table would contain all transaction data, plus a member id.
So, one member can have many transactions.
MEMBERS
id, username, password
1, gravy, ****
2, john, ****
3, mike, ****
TRANSACTIONS
id, memberid, ticket_date, ticket_num, ticket_result
1, 1, 2014/05/07, 57, 1
2, 2, 2014/05/07, 58, 1
3, 3, 2014/05/07, 59, 1
4, 1, 2014/05/07, 60, 1
5, 3, 2014/05/07, 61, 1
You match the data from both tables
Gravy bought 2 tickets (57 and 60)
John bought 1 ticket (58)
Mike bought 2 tickets (59 and 61)
So by searching for all transactions in the transaction table which have a memberid of #, you can get all the transactions by user #. In this example Gravy was user #1 and therefore all the transactions in the transaction table with memberid 1, were transcations made by Gravy.
You really should read a book about relational databases.