Question

Use the Gram-Schmidt process to transform the basis



[1
1
1]
,

[0
1
1]
,

[2
4
3]


for the Euclidean space R3 into an orthonormal basis for R3. (Enter each vector in the form [x1, x2, ...]. Enter your answers as a comma-separated list.)

so i went through the process and got

[1/sqrt(3),1/sqrt(3),1/sqrt(3)],[-2/sqrt(6),1/sqrt(6),1/sqrt(6)],[-7/sqrt(62),-2/sqrt(62),-3/sqrt(62)]
You have u1 and u2 correct. Don't know if you're expected to rationalize the denominator, in which case, u1 would read
[(√3)/3,(√3)/3,(√3)/3]...etc.

u3 should be [0,....]

A good way to check your answer is to verify if u1.u2=0, u1.u3=0, u2.u3=0.

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