Mathematics, 03.05.2021 20:50 alexusdyer94
Do the given vectors form an orthogonal basis for โ3? v1 = 1 0 โ1 , v2 = 2 4 2 , v3 = 3 โ3 3 Yes, the given set does form an orthogonal basis for โ3. No, the given set does not form an orthogonal basis for โ3. You are given the theorem below. Let {v1, v2, , vk} be an orthogonal basis for a subspace W of โn and let w be any vector in W. Then the unique scalars c1, , ck such that w = c1v1 + + ckvk are given by ci = w ยท vi vi ยท vi for i = 1, , k. Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w]basis B of w with respect to the basis basis B = {v1, v2, v3} of โ3. w = 1 1 1 [w]basis B =
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Do the given vectors form an orthogonal basis for โ3? v1 = 1 0 โ1 , v2 = 2 4 2 , v3 = 3 โ3 3 Yes, th...
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