Problem 1 Consider the following function:

??(??) = ?? ? 3 cos(??)

a) Prove that there exists at least one root in the interval [0 2??]

b) Apply 2 steps of bisection method to approximate the root. Give your best estimate at the end

Problem 2 Consider the following system of linear equations:

3?? + ?? ? ?? = 2 ?? ? 2?? + ?? = 0 5?? ? 2?? = ?1

a) Show how to write these equations in the matrix form ???? = ??

b) Determine and verify the inverse of matrix ?? by hand. Show the steps.

c) Use the result from part b to find the unknowns: ??, ??, y