# Quiz Chapter 06: Gaussian Elimination

 MULTIPLE CHOICE TEST GAUSSIAN ELIMINATION

Pick the most appropriate answer

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