For this week's laboratory, you will write four linear algebra functions usingfor-loops or while-loops. The four linear algebra functions you will write are1) calculating the magnitude of a vector, 2) a vector dot product, 3) matrix-vector multiply (Ax-bi, and4) matrix-matrix multiply (AB=C). You will write your programs in JupyterNotebook. You will define the input vectors and matrices in the main, passinto your functions, and pass out the results (i.e. magnitude of a vector, theresult from the dot product, the result from the matrix-vector multiply, whichis the vector b, and the result from the matrix-matrix multiply, which is thematrix C). You cannot use any built-in mathematical functions; you mustwrite these on your own.Below are the vectors and the matrix you will use81-4 15275176 32301 82112209271x₁=and x2=A=and B=1011106 111411223241761794 23824 227

Magnitude of a Vector: Calculating the magnitude (or length) of a vector.Vector Dot Product:…

Answered: For this week's laboratory, you will…

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter7: Arrays

Section: Chapter Questions

Problem 3PP: (Numerical) Given a one-dimensional array of integer numbers, write and test a function that...

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(Electrical eng.) a. An engineer has constructed a two-dimensional array of real numbers with three rows and five columns. This array currently contains test voltages of an amplifier. Write a C++ program that interactively inputs 15 array values, and then determines the total number of voltages in these ranges: less than 60, greater than or equal to 60 and less than 70, greater than or equal to 70 and less than 80, greater than or equal to 80 and less than 90, and greater than or equal to 90. b. Entering 15 voltages each time the program written for Exercise 7a runs is cumbersome. What method could be used for initializing the array during the testing phase? c. How might the program you wrote for Exercise 7a be modified to include the case of no voltage being present? That is, what voltage could be used to indicate an invalid voltage, and how would your program have to be modified to exclude counting such a voltage?
(Numerical) Using the srand() and rand() C++ library functions, fill an array of 1000 floating-point numbers with random numbers that have been scaled to the range 1 to 100. Then determine and display the number of random numbers having values between 1 and 50 and the number having values greater than 50. What do you expect the output counts to be?
(Statistics) a. Write a C++ program that reads a list of double-precision grades from the keyboard into an array named grade. The grades are to be counted as they’re read, and entry is to be terminated when a negative value has been entered. After all grades have been input, your program should find and display the sum and average of the grades. The grades should then be listed with an asterisk (*) placed in front of each grade that’s below the average. b. Extend the program written for Exercise 1a to display each grade and its letter equivalent, using the following scale: Between90and100=AGreaterthanorequalto80andlessthan90=BGreaterthanorequalto70andlessthan80=CGreaterthanorequalto60andlessthan70=DLessthan60=F
(Numerical) Write and test a function that returns the position of the largest and smallest values in an array of double-precision numbers.
(Data processing) Your professor has asked you to write a C++ program that determines grades at the end of the semester. For each student, identified by an integer number between 1 and 60, four exam grades must be kept, and two final grade averages must be computed. The first grade average is simply the average of all four grades. The second grade average is computed by weighting the four grades as follows: The first grade gets a weight of 0.2, the second grade gets a weight of 0.3, the third grade gets a weight of 0.3, and the fourth grade gets a weight of 0.2. That is, the final grade is computed as follows: 0.2grade1+0.3grade2+0.3grade3+0.2grade4 Using this information, construct a 60-by-7 two-dimensional array, in which the first column is used for the student number, the next four columns for the grades, and the last two columns for the computed final grades. The program’s output should be a display of the data in the completed array. For testing purposes, the professor has provided the following data:
(Practice) Write specification statements for the following: a. An array of integers with 6 rows and 10 columns b. An array of integers with 2 rows and 5 columns c. An array of characters with 7 rows and 12 columns d. An array of characters with 15 rows and 7 columns e. An array of double-precision numbers with 10 rows and 25 columns f. An array of double-precision numbers with 16 rows and 8 columns
(Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.
(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ft
(Electrical eng.) Write a program that specifies three one-dimensional arrays named current, resistance, and volts. Each array should be capable of holding 10 elements. Using a for loop, input values for the current and resistance arrays. The entries in the volts array should be the product of the corresponding values in the current and resistance arrays (sovolts[i]=current[i]resistance[i]). After all the data has been entered, display the following output, with the appropriate value under each column heading: CurrentResistance Volts
(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.
(Practice) Write correct notation for the first, third, and seventh elements of the following arrays: a. int grades[20] b. double volts[10] c. double amps[16] d. int dist[15] e. double velocity[25] f. double time[100]
(Numerical) a. The following is an extremely useful programming algorithm for rounding a real number to n decimal places: Step 1: Multiply the number by 10n Step 2: Add 0.5 Step 3: Delete the fractional part of the result Step 4: Divide by 10n For example, using this algorithm to round the number 78.374625 to three decimal places yields: Step1:78.374625103=78374.625 Step2:78374.625+0.5=78375.125 Step3:Retainingtheintegerpart=78375Step4:78375dividedby103=78.375 Using this algorithm, write a C++ function that accepts a user-entered value and returns the result rounded to two decimal places. b. Enter, compile, and run the program written for Exercise 11a.

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