00:01
Hi, now we are going to find the arthonormal basis.
00:04
The given standard bases are 1 comma x.
00:08
X cube and the given condition is inner product f comma g is equal to integral over minus 1 to 1 to 1 f of x into g of x into dx.
00:28
Now i take v1 is equal to 1 and v2 is equal to x and v3 is equal to x cube.
00:40
W1 is equal to v1.
00:43
So we have w1 is equal to 1.
00:48
And next we are going to calculate w2.
00:52
W2 is equal to v2 minus inner product.
00:59
V2 comma w1 divide by norm of w1 into w1.
01:09
Now we are going to calculate inner product v2 comma w1 and it will be equal to inner product x comma 1 that is integral over minus 1 to 1 x d x.
01:30
After integration and substituting the limits, it will be equal to 0.
01:36
And next, norm of w1 is equal to integral over minus 1 to 1 -d -x and it will be equal to 2.
01:52
Now substitute the corresponding values in the w -2 formula.
01:56
Then we have w -2 is equal to x minus 0 divide by 2...