# Quiz Chapter 06: Gaussian Elimination

 MULTIPLE CHOICE TEST GAUSSIAN ELIMINATION

1. The goal of forward elimination steps in Naïve Gauss elimination method is to reduce the coefficient matrix to a(n) ______ matrix.

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

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

• $0.0030x_{1} + 55.23x_{2} = 58.12$
• $6.239x_{1} - 7.123x_{2} = 47.23$

is

4. Using a computer with four significant digits with chopping, Gaussian elimination  with partial pivoting solution to

• $0.0030x_{1} + 55.23x_{2} = 58.12$
• $6.239x_{1} - 7.123x_{2} = 47.23$

is

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

$\begin{bmatrix} 4.2857 \times 10^{7}&-9.2307 \times 10^{5}&0&0 \\ 4.2857 \times 10^{7}&-5.4619 \times 10^{5}&-4.2857 \times 10^{7}&5.4619 \times 10^{5} \\ -6.5&-0.15384&6.5&0.15384 \\ 0&0&4.2857 \times 10^{7}&-3.6057 \times 10^{5} \\ \end{bmatrix} \begin{bmatrix}c_{1} \\ c_{2} \\ c_{3} \\c_{4} \\ \end{bmatrix} = \begin{bmatrix} -7.887 \times 10^{3} \\ 0 \\ 0.007 \\ 0 \\ \end{bmatrix}$

the resulting equations in the matrix form are given by

$\begin{bmatrix} 4.2857 \times 10^{7}&-9.2307 \times 10^{5}&0&0 \\ 0&3.7688 \times 10^{5}&-4.2857 \times 10^{7}&5.4619 \times 10^{5} \\ 0&0&-26.9140&0.579684 \\ 0&0&0&5.62500 \times 10^{5} \\ \end{bmatrix} \begin{bmatrix}c_{1} \\ c_{2} \\ c_{3} \\c_{4} \\ \end{bmatrix} = \begin{bmatrix} -7.887 \times 10^{3} \\ 7.887 \times 10^{3} \\ 1.19530 \times 10^{-2} \\ 1.90336 \times 10^{4} \\ \end{bmatrix}$

The determinant of the original coefficient matrix is

6. 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, $v(t) = at^{2} + bt + c$ to approximate the velocity profile.

 $t$ (s) $0$ $14$ $15$ $20$ $30$ $35$ $v(t)$ m/s $0$ $227.04$ $362.78$ $517.35$ $602.97$ $901.67$

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