(c) Find the least squares solution to the problem ar₁ = b for the one unknown ₁ where a and b are column vectors of length m. In this way find the least squares approximation for the unknown scalar A to the equations Ax = xx where x is a given m-dimensional vector and A is a given m x m matrix. The result is known as the Rayleigh-quotient approximation for the eigenvalue X given an approximate eigenvector x.

can someone explain how we get to the numbers 476,-84,-252

How do I solve this in steps?

https://www.youtube.com/watch?v=pnO6qC-6Shg

Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0). => √27 + => (smaller i-value) 5k √27 √27 X (larger i-value)

Describe all least-squares solutions of the equation Ax = b. 110 1 1 1 0 5 A = #-0 10 1 4 101 8 The least-squares solutions are all vectors of the form x = (Simplify your answers.) +x3, with x3 free.

2 0 1 4 5 30x3 = 43 = (25² 0 ..] Can we use Cramer's Rule to check if the column vectors of A are linearly (in)dependent? Explain why or why not and regardless, identify all linearly independent column vectors in A. *Derive the vector x3 in Ax3 = b by two different methods (please show the essential calculations- outlining the method(s) isn't enough to get you credit).