00:01
Hi, given b is equal to b1 b2 and c is equal to c1 c2 b basis for r2.
00:10
Now we have to find change of coordinates matrix from b to c and then from c to b.
00:14
So b1 vector is minus 2 minus 4, b2 vector is 3 8, c1 vector is 6 8 and c2 vector is minus 13 and 18.
00:25
So now from b to c.
00:29
So c matrix b matrix so 6 8 minus 13 minus 18 minus 2 minus 4 3 and 8.
00:38
So we first we will make this identity matrix.
00:43
So we first apply the operation r1 goes to r1 by 6.
00:47
So we have 1 minus 13 by 6 minus 1 by 3 and 1 by 2 and over here 8 minus 18 minus 4 and 8 r2 as it is.
01:02
Next we apply the operation r2 goes to r2 minus 8 times r1.
01:08
So this is equal to 1 minus 13 by 6 minus 1 by 3 1 by 2 0 minus 2 by 3 minus 4 by 3 and 4.
01:19
Next we apply r2 goes to minus 3 by 2 times r2 to make this 1.
01:25
So this will be equal to 1 minus 13 by 6 minus 1 by 3 1 by 2 0 1 2 and minus 6 and then we apply operation r1 goes to r1 plus 13 by 6 times r2.
01:40
So this is further equal to 1 0 0 1 and 4 minus 25 by 2 2 and minus 6.
01:53
So in this case the change of coordinate matrix becomes b b to c as 4 2 minus 25 by 2 and minus 6...