Using matlab please give the code for this assignment:

Major Assignment $2$

Due Friday, November $15$ by $11$:$59$ pm

The purpose of this major assignment is to consolidate your knowledge of the material on systems of

linear equations and MATLAB functions covered up to this point.

You should submit one Matlab file following this naming format: major$2\_$ID#$.$m

$($e$.$g$.,$ major$2\_123456789.$m$)$

Problem

Traffic incident duration is a measure of the time required to detect, respond, and clear an incident from

the road. Examples of these incidents include collisions, broken vehicles, fallen trees, among others. As

demonstrated in the breakdown above, the incident duration can be calculated as the sum of its time

components $($denoted T$1,$ T$2,$ and T$3).$

The following system of equations relates the time components $($measured in seconds$)$ of the incident

duration to three major factors that have a strong impact:

$1=0\mathrm{.}015+4\mathrm{.}733\mathrm{.}81$

$2=0\mathrm{.}0930\mathrm{.}810\mathrm{.}77$

$3=0\mathrm{.}0380\mathrm{.}56+17\mathrm{.}55$

Where V is the traffic volume in vehicles per hour $($vph$),$ S is the average vehicle speed on the road in

km$/$h$,$ and L is the number of lanes blocked by the incident.

Task $1$

If the time components of a recently recorded incident were measured as T$1=197\mathrm{.}76$ s$,$ T$2=179\mathrm{.}42$ s$,$ and

T$3=97\mathrm{.}36$ s$,$ what are the corresponding factors $($volume$,$ speed, and lanes blocked$)$ at the time of the

incident? To answer this, write a multi$-$line function that uses the Gauss Elimination method to solve the

system of equations and retrieve the values of the three factors. $[$Use variable names of A $=$ matrix of

coefficients, B $=$ vector of equation values, XGauss $=$ solution vector$].$

Page $2$ of $2$

Task $2$

Solve the system of equations from Task $1$ using a built$-$in MATLAB command to find XMat, and check

$($using an IF statement$)$ if the answer matches your Gauss Elimination solution. Your check should

conclude that the Gauss Elimination solution is accurate only if the error summation of all three calculated

factors does not exceed a tolerance of $0\mathrm{.}1\%.$

Task $3$

Assuming that the system of equations has been tested for a finite range of values of the three factors $($V$,$

S$,$ and L$),$ what are all the possible incident durations that can be calculated with this system?

Factor Unit Range Step size Total scenarios

Volume $($V$)$ vph $500-350010031$

Speed $($S$)$ km$/$h $10-100519$

Lanes blocked $($L$)-1-414$

The table above lists the range, step size, and the subsequent number of possible scenarios for each of

the three factors. Using nested loops, create a vector called $$durations$$ of all the possible values of

incident duration. Include a check that verifies if any of T$1,$ T$2,$ or T$3$ are negative, and changes the negative

value to zero. Then find the minimum and maximum incident durations $($in minutes$)$ of the developed

vector.

Task $4$

Print to the command window only the following with the blanks filled automatically from your coded

solution:

Using Gauss Elimination, the time components of the reported incident indicate that the

traffic volume was $\_\_\_\_\_$ vph$,$ the average speed was $\_\_\_\_\_$ km$/$h$,$ and $\_\_\_\_\_$number of

lanes were blocked.

Validation using MATLAB$$s built$-$in functions revealed that the Gauss Elimination method

was $($accurate$/$inaccurate$).$

In total, there were $\_\_\_\_\_$ possible scenarios of incident duration that could be solved

using the system of equations, with a minimum of $\_\_\_\_\_$ min and a maximum of $\_\_\_\_\_$