00:01
Hello, let's have a look at the question.
00:03
So the question state let t is defined in r2 to r2 be a linear transformation and suppose that we have t at 1, 0 is equals to 3, 5 and t at 0, 1 is equals to 2, 7 and we have to find the matrix for t.
00:29
So first of all let it be the first equation and this is the second equation where 1, 0 and 0, 1 are the standard basis of r2.
00:52
So now here we have to write 3 by 5 as a linear combination of 1, 0 and so therefore we can write 3, 5 is equals to a multiplied with 1, 0 and added with b 0, 1.
01:12
So therefore here we get 3, 5 is equals to a, b and here we get that the value for a is equals to 3 and the value for b is equals to 5.
01:26
Therefore we can write that 3, 5 can be written as 3 multiplied with 1, 0 added with 5, 0, 1.
01:39
Now similarly we can write so 2, 7 can be written as a linear combination of 1 and 0 and 0 and 1.
01:49
So this will be c multiplied with 1, 0 added with d multiplied with 0, 1...