00:01
Hi, here in this question using the gram segment process we need to find the value of orthonormal and orthogonal basis we have u1 equals to 121 similarly u2 equals to 8 1 and 6 and the value of u3 equals to 0 0 and 1 now here we know that formula to calculate w1 equals to u1 upon magnitude of u1 now here let v equals to u1 upon norm of u1 therefore here in our case the norm of u1 is equal to under root 6 therefore here using the values and simplifying further we have w1 equals to 0 .67 1 .33 and again 0 .67.
01:07
Now further we need to calculate what is the value of v2 let v2 equals to u2 minus dot product of w 1 into u2 again multiplied with w 1 now here first of all we will find the value of v2 and then we will find the norm of the p2 vector so here using all this value and doing the dot product we have v2 equals to 7 .33 minus 0 .33 and minus 6 .67 now here for w2 we have v2 upon norm of vector v2 so simplifying this here we have w2 equals to 0 .6 .6 .7.
01:57
Now here for w2 we have w2 equals to 0 .5 .5.
01:57
So simplifying this here we have w2 equals to 0 .4.
02:01
Minus 0 .03 and minus 0 .67.
02:06
Similarly, we need to calculate the value of v3.
02:10
So here in our case, we have v3 equals to u3 minus w1 multiplied with u3 again multiplied with w1 minus w2 multiplied with u2, u3 multiplied with w2.
02:30
So here, substituting the values and simplifying this, we have v3 equals to minus 0 .17 minus 0 .33 and 0 .83...