مهندسی شیمی-موازنه مواد و انرژی

Q1. The goal of forward elimination steps in the Naïve Gauss elimination method is to reduce the coefficient matrix to a (an) _____________  matrix.

diagonal

identity

lower triangular

upper triangular

Q2. Division by zero during forward elimination steps in Naïve Gaussian elimination of the set of equations [A][X]=[C] implies the coefficient matrix [A] is

invertible

nonsingular

not determinable to be singular or nonsingular

singular

Q3. Using a computer with four significant digits with chopping, Naïve Gauss elimination solution to

is

x₁ = 26.66; x₂ = 1.051

x₁ = 8.769; x₂ = 1.051

x₁ = 8.800; x₂ = 1.000

x₁ = 8.771; x₂ = 1.052

Q4. Using a computer with four significant digits with chopping, Gauss elimination with partial pivoting solution to

is

  x₁ = 26.66; x₂ = 1.051

  x₁ = 8.769; x₂ = 1.051

  x₁ = 8.800; x₂ = 1.000

  x₁ = 8.771; x₂ = 1.052

Q5. At the end of forward elimination steps of Naïve Gauss Elimination method on the following equations

the resulting equations in the matrix form are given by

The determinant of the original coefficient matrix is

0.00

Q6. The following data is given for the velocity of the rocket as a function of time.  To find the velocity at t=21 s, you are asked to use a quadratic polynomial, v(t)=at²+bt+c to approximate the velocity profile.

The correct set of equations that will find a, b and c are