00:01
Hello everyone, in this problem we are given with the transformation t is from r2 to r2 which is a linear transformation that satisfies t of 1 ,3 to be equal to 3 ,1 and t of 2 ,5 which is equal to 1 ,2.
00:22
Now we need to find the value of t of x ,y.
00:26
So for that we consider 1 ,0 to be equal to 3 of 2 ,5 minus 5 of 1 ,3.
00:37
So now taking transformations on both sides so t of 1 ,0 which is equal to 3 of 3 multiplied by t of 2 ,5 minus 5 multiplied by t of 1 ,3.
00:52
So from this given we can rewrite t of 2 ,5 to be t of 1 ,2 so 3 multiplied by 1 ,2 minus 5 multiplied by t of 1 ,3 can be written as 3 ,1.
01:04
So now multiplying this it will become 3 ,6 minus 15 ,5.
01:13
So now subtracting these two values according to its coordinate value so it will be minus 12 ,1.
01:20
So we have the value of t of 1 ,0 to be minus 12 ,1.
01:27
So now we can also find 0 ,1 as 2 multiplied by 1 ,3 minus 1 multiplied by 2 ,5.
01:44
So now taking transformation on both sides so t of 0 ,1 it will become 2 multiplied by t of 1 ,3 minus t multiplied by 2 ,5.
01:56
So now we can rewrite this from the given so it will be 2 multiplied by 3 ,1 minus 12.
02:05
So now substituting multiplying this it will become 6 ,2 minus 12...