Question

Find the closest point to y in the subspace W spanned by u1​ and u2​. y=⎣⎡​11922​⎦⎤​,u1​=⎣⎡​22−1​⎦⎤​,u2​=⎣⎡​−134​⎦⎤​ ⎣⎡​6144​⎦⎤​ ⎣⎡​01614​⎦⎤​ ⎣⎡​−89695​⎦⎤​ ⎣⎡​0−16−14​⎦⎤​

Answer 1

To find the closest point to y in the subspace W spanned by u1 and u2, we can use the projection formula.

Step-by-step explanation:

To find the closest point to y in the subspace W spanned by u1 and u2, we can use the projection formula. Let's denote the closest point as p. The projection of y onto W can be found using the formula:

p = ((y·u1)/(u1·u1)) * u1 + ((y·u2)/(u2·u2)) * u2

Substituting the given values, we have:

p = (2/6) * (22, -1) + (-5/6) * (-13, 4)

Calculating the values, we get p = (8/3, 7/3).