"They are a very balanced team and we have to be at our best to beat them, it's a huge challenge," said Mathews who has been in top form since being named the captain last February.
The second and final Test will be played in Colombo from July 24-28.
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On Monday, Jayawardene announced he will retire from the longest format of the game in August, after the two-Test rubber against South Africa followed by two matches against Pakistan (Aug 6-18).
The 37-year-old right hander will only be available for one-day internationals, having also retired from Twenty20 cricket in April this year.
"We need a player like him in the team, but he (Jayawardene) has decided to say goodbye," Mathews said at a pre-match press conference in Galle on Tuesday.
"If we can send him off by winning all four Tests it will be great