I look at your problem and I think I solve it.
Basically there is two problems here first one is to pivot your table where your Tran_Qtyx column become Qty_In and Qty_Out based on value in Tran_Type column (IN or OUT)... That part of problem you solve with this query
SELECT Tran_Date, Mate_Code,
SUM(CASE WHEN Tran_Type = 'IN' THEN Tran_Qtyx ELSE 0 END) Qty_In,
SUM(CASE WHEN Tran_Type = 'OUT' THEN Tran_Qtyx ELSE 0 END) Qty_Out
FROM myTable
WHERE Mate_Code = 'MAT001'
GROUP BY DATE(Tran_Date)
NOTE: In your desired result I only see 'MAT001'as Mate_Code so I stick with that in this solution and exclude MAT002 from result.
More about pivot table you can read here, there you can find a link, which is good to take a look, and where you can find a lot of stuff about mysql query's.
The second part of your problem is to get Qty_Balance column. Similar problem is solved here. It's how to calculate row value based on the value in previous row.
So your complete query could look like this:
SELECT t1.Tran_Date, t1.Mate_Code, t1.Qty_In, t1.Qty_Out,
@b := @b + t1.Qty_In - t1.Qty_Out AS Qty_Balance
FROM
(SELECT @b := 0) AS dummy
CROSS JOIN
(SELECT Tran_Date, Mate_Code,
SUM(CASE WHEN Tran_Type = 'IN' THEN Tran_Qtyx ELSE 0 END) Qty_In,
SUM(CASE WHEN Tran_Type = 'OUT' THEN Tran_Qtyx ELSE 0 END) Qty_Out
FROM myTable
WHERE Mate_Code = 'MAT001'
GROUP BY DATE(Tran_Date)) AS t1
ORDER BY t1.Tran_Date;
NOTE: probably only think you should change here is table name and it's should work.
Here is SQL Fiddle so you can see how that's work!
GL!