Least squares and qr factorization. suppose a is an m n matrix with linearly independent columns and qr factorization a = qr, and b is an m-vector. the vector a^x is the linear combination of the columns of a that is closest to the vector b, i. e., it is the projection of b onto the set of linear combinations of the columns of a. (a) show that a^x = qqt b. (the matrix qqt is called the projection matrix.) (b) show that = bk2. (this is the square of the distance between b and the closest linear combination of the columns of a.)

answer: sensy

step-by-step explanation:

0.32

step-by-step explanation:

2.24/7

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.