Let A be an n × n nonsingular matrix. (a) Find the number of arithmetic operations for the LU factorization, which is based on the Gaussian elimination with partial pivoting. [Note: To compare two numbers, say, a and b, we need to perform the subtraction a - b and then check the sign of the result. So, finding the maximum of k numbers, requires k – 1 subtractions.] (b) Find the number of arithmetic operations required to find the inverse matrix A-¹ using the LU factorization from part (a). [Note: The LU factorization needs to be performed only once.] (c) Suppose that A-¹ has been calculated. Find the number of arithmetic operations required to compute the multiplication A-¹b. [Note: Combine multiplications/divisions and additions/subtractions together.]

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