### Matrix Questions for Understanding Row Echelon Form#### Question 40**a.** If \(A\) is a matrix with three rows and five columns, then what is the maximum possible number of leading 1’s in its reduced row echelon form?**b.** If \(B\) is a matrix with three rows and six columns, then what is the maximum possible number of parameters in the general solution of the linear system with augmented matrix \(B\)?**c.** If \(C\) is a matrix with five rows and three columns, then what is the minimum possible number of rows of zeros in any row echelon form of \(C\)?

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Answered: 40. a. If A is a matrix with three rows…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. For each part, write a matrix in reduced row echelon with the given properties. Your answers must have at least 2 rows and at least 2 columns. If such a matrix is not possible, state why. (a) Is always solvable and 2 dependent variables. (b) Has a unique solution and columns are spanning. (c) Columns are dependent and the transformation is one-to-one. (d) Has more rows than columns and the transformation is onto.
The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. A. The solution has infinitely many elements. B. The solution set contains one solution: (411) (Type integers or simplified fractions.) 1 -1 0 0 0 1 3 0 0 1 0 001 OC. The solution set is empty. I - 2 4 0-6 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. 2 3
Assume that the following augmented matrix represents a system of linear equations. -1 -8 2 -1 -2 -20 -8 -1 -1 -14-3 What kind of solution does this system have? (A) infinitely many solutions with 2 arbitrary (free) parameters (B) 3 solutions (C) infinitely many solutions with 1 arbitrary (free) parameter (D) 2 solutions (E) unique solution (F) infinitely many solutions with 4 arbitrary (free) parameters (G) infinitely many solutions with 3 arbitrary (free) parameters (H) no solution A O B O E G H
Suppose the coefficient matrix associated with a linear system has a pivot in each row. Can we say, with certainty, that the linear system is consistent or inconsistent? Defend your response.
15 ) good handwriting please
5. For the given system, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involve not free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. X1 2x2 = 3 2x1 X2 = 9 -
6. Suppose the augmented matrices below correspond to either a system of linear equa- tions in 2 variables (x, y) or system of linear equations in 3 variables (x, y,z). These matrices may or may not be in RREF. You you need to in order to determine the solutions. NOT need to put them into RREF unless What are the solutions to the system? If there are solutions, please write your answer as (x, y) or (x, y,z). If there are infinitely many solutions, please write your point in terms of one variable (you may choose the variable). 1 0 0 1 -7 0 0 2 (a) 1 -6 1 0 0 0 1 0-4 0 0 1 9 (b) 9 1 0 (c) 0 1 -4 0 0 1 0 -4 (d) 0 1 -3 1 5 7 0 0 0 0 0 0 (e)
33 please
The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. 1 -2 0 - 5 1 - 1 - 6 1 - 3 3 0 0 0 1 4 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The solution set is empty. В. The solution set contains one solution: ( , | | D. (Type integers or simplified fractions.) O C. The solution has infinitely many elements.

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