00:01
Hi, let's start the solution.
00:02
In this question, we have given matrix a is minus 1 2 minus 1 2 minus 3 3 and b is 4 2 3.
00:16
Here order of matrix a is 3 cross 2.
00:21
Then we have to find the least square solution of ax equal to b.
00:40
So first by constructing normal equation.
00:44
Now compute a transpose a which is equal to a transpose means interchange row and columns.
01:00
Then we get minus 1 2 minus 1 2 minus 3 3 and a is minus 1 2 minus 1 2 minus 3 3.
01:15
So by multiplying these two matrix here we get which is equal to 6 minus 11 minus 11 22.
01:24
So we get here a transpose a is 6 minus 11 minus 11 22.
01:34
Now we compute a transpose into b.
01:38
A transpose is minus 1 2 minus 1 2 minus 3 3 and b is 4 2 3.
01:47
By multiplying this here we get which is equal to minus 3 11.
01:53
So we get here a transpose b is minus 3 11.
01:58
So that means normal equation is a transpose a into x equal to a transpose b.
02:18
So we get here vector x cap x cap that is.
02:23
So a transpose a is 6 minus 11 minus 11 22 and this one is x 1 x 2 which is equal to a transpose b is minus 3 11...