Find the closest point to y in the subspace w spanned by bold v 1v1 and bold v 2v2. yequals=left bracket start 4 by 1 matrix 1st
row 1st column negative 15 2nd row 1st column negative 1 3rd row 1st column 1 4st row 1st column 2 endmatrix right bracket −15 −1 1 2 , bold v 1v1equals=left bracket start 4 by 1 matrix 1st row 1st column 1 2nd row 1st column 1 3rd row 1st column negative 1 4st row 1st column negative 2 endmatrix right bracket 1 1 −1 −2 , bold v 2v2equals=left bracket start 4 by 1 matrix 1st row 1st column 5 2nd row 1st column 1 3rd row 1st column 0 4st row 1st column 3 endmatrix right bracket
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Answer:
b = 9
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² + 12² = 15²
b² + 144 = 225 ( subtract 144 from both sides )
b² = 81 ( take the square root of both sides )
b = = 9