Gramm Schmidt question

Hello members,

Just to conclude my math home assignment. I am trying to work out question 4 and I am having a difficulty to calculate the weights( as seen at the end of pdf) on my solution. Weight one became negative and weight two became is positive but the weights should be both positive. I tried several times checking my working using Wolfram Alpha. but with no success. Please could someone help me to locate my mistakes that I can't see?

Again thank you,
Saviour