Describe at least three distinct ways to solve a system of equations using linear algebra. (Distinct...

Describe at least three distinct ways to solve a system of equations using linear algebra. (Distinct means that the approach is fundamentally different.) Be specific and detailed using linear algebra vocabulary. It might be helpful to pick an example problem and illustrate each of the three methods.

Suppose T1 and T2 are linear transformations from Rn to Rn. Let T(x) = T2(T1(x))

The responses should be very clear like you are writing instructions to someone who doesn’t know the process.

Describe how to find the transformation matrix of T1.

Describe how to find the transformation matrix of T. (Bonus +2 points if you can describe a second method.)

Is T2(T1(x)) = T1(T2(x)) for any linear transformation T1 and T2? Explain.

Expert Solution

Colby Messinger answered 2 years ago

Use Java (Algebra: solve 2 x 2 linear equations) A linear equation can be solved using...

Use Java (Algebra: solve 2 x 2 linear equations) A linear equation can be solved using Cramer’s rule given in Programming Exercise 1.13. Write a program that prompts the user to enter a, b, c, d, e, and f and displays the result. If ad - bc is 0, report The equation has no solution. Sample Run 1 Enter a, b, c, d, e, f: 9.0 4.0 3.0 -5.0 -6.0 -21.0 x is -2.0 and y is 3.0 Sample Run...

Hello. Linear Algebra class. In a linear system of equations, the solution is one of the...

Hello. Linear Algebra class. In a linear system of equations, the solution is one of the possibilities. 1)there is one unique solution(only one) which means the line of the equation interest only one time at a point. 2)there are many solutions (infinity) if the lines of equations lie on one another. 3)there is no solution if the line of the equation are parallel. how to test for each possibility WITHOUT graphing the system of equations using the coefficients in each...

Write a python program that can solve system of linear equations in three variables using input...

Write a python program that can solve system of linear equations in three variables using input function. Paste your program in a word document or notepad. Note that I am using pycharm. please use a not really complex codes, thanks

1) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no...

1) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) 3y + 2z = 1 2x − y − 3z = 4 2x + 2y − z = 5 (x, y, z) = 2) Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION....

Write a function to solve a system of linear equations of the form Ax= b using...

Write a function to solve a system of linear equations of the form Ax= b using the iterative Gauss-Seidel method. You are free to use any basic MATLAB operation to implement the algorithm (i.e. you may use any combination of loops, indexing, math, etc.), but avoid “built-in” solution methods — you would not be allowed to use the GaussSeidel function if such a function existed. The function must also test for a number of possible issues. If an issue is...

SET UP BUT DO NOT SOLVE the following system of linear equations: A company sells three...

SET UP BUT DO NOT SOLVE the following system of linear equations: A company sells three sizes of fruit trays. The small size contains 200 gr of watermelons and 100 gr of grapes. The medium size contains 400 gr of watermelons, 100 gr of pineapples, and 300 gr of grapes. The large size contains 600 gr of watermelons, 200 gr of pineapples, and 400 gr of grapes. Suppose that the company receives an order for 28 kg of watermelons, 6...

Solve the system of linear equations using partial pivoting. 144a1 + 12a2 + a3 = 279.2...

Solve the system of linear equations using partial pivoting. 144a1 + 12a2 + a3 = 279.2 64a1 + 8a2 + a3 = 177.2 25a1 + 5a2 + a3 = 106.8

When using Gaussian elimination to solve a system of linear equations, how can you recognize that...

When using Gaussian elimination to solve a system of linear equations, how can you recognize that the system has no solution?

Write your own routine to solve a system of n linear equations and n unknowns using...

Write your own routine to solve a system of n linear equations and n unknowns using the LU decomposition. Input should take an augmented matrix and the number of equations n. Output should be the augmented matrix. L and U matrices and the solution. Also compare your results to those of Matlab’s built in LU decomposition. Use your code to solve the systems given as (a) and (b) below: a) 3a − 2b + c = −3, a − 4b...

Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 2y + z...

Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 2y + z = 3 x + z = 2 4y − 3z = 13 solve for x,y,x

Question