#65 12:54Done elementary_linear_algebra_8th_edi...number of cach denomination.A System of Linear Equations In Exercises 39-42, useOa software program or a graphing utility to solve thesystem of linear equations.Matrix Representation In Exercises 49 and 50, assumethat the matrix is the augmented matrix of a systemof linear equations, and (a) determine the number ofequations and the number of variables, and (b) find thevalue(s) of k such that the system is consistent. Thenassume that the matrix is the coefficient matrix of ahomogeneous system of linear equations, and repeatparts (a) and (b).39. X, - 2x, + 5x, - 3x, - 23.6X, + 4x, - 7x, - 2x, - 45.73x, - Sx, + 7x, + 4,- 29.940. X, + - 2x, + 3, + 2x, -93x, + 3x, - x, + + , 52x, + 2x, - x, + x- 2r, - 14x, + 4, + x,&r, + Sx, - 2x, - ,+ 2x, - 341. x, - x, + 2x, + 2r, + 6r,- 63x, - 2x, + 4x, + 4x, + 12, 14X- - - 3,- -32x, - 2x, + 4x, + Sx, + 15x, - 102r, - 2x, + 4x,+ 4x, + 13x, - 1342. X, + 2x, - 2x, + 2x, - X, + 3,- 02x,- x + 3x, + - 3x, + 2x, - 17X + 3x, - 21, + - 2x, - 3x,- -53x, - 2x, + x, - x + 3x, - 2x, --1-X, - 2x, + X+ 2x, - 2x, + 3- 10X, - 3x, + , + 3x, - 2x, + -II249. A-- 3,-4-322 -1 350. A--44 -2Coefficient Design In Exercises 51 and 52, find valuesof a, b, and e (if possible) such that the system of linearequations has (a) a unique solution, (b) no solution, and(e) infinitely many solutions.51. x+ y-252. + v-0y+ -2* + :- 2ar + by + cz -0y+ -0* +-0ar + by + cz = oCe tcel ey C24Chapter 1 Systems of Linear Equations53. The system below has one solution: x= 1. y= -1,and : - 2.61. Writing Is it possible for a system of linear equationswith fewer equations than variables to have no solution?If so, give an example.62. Writing Does a matrix have a unique row-echelonform? Illustrate your answer with examples.4x - 2y + 5z = 16Equation IEquation 2-x- 3y + 2:- 6 Bquation 3I+ y -0Row Equivalence In Exercises 63 and 64, determineSolve the systems provided by (a) Equations I and 2,(b) Equations I and 3, and (c) Equations 2 and 3.(d) How many solutions does each of these systemshave?conditions on a, b, c, and d such that the matrix54. Assume the system below has a unique solution.will be row-equivalent to the given matrix.a + a, + a,-b,a + a + at- b;ak, + a + al = b,Equation IEquation 2Equation 363. : |64.Homogeneous System In Exercises 65 and 66, findall values of A (the Greek letter lambda) for which theDoes the system composed of Equations I and 2 havea unique solution, no solution, or infinitely manysolutions?homogeneous linear system has nontrivial solutions.65. A - 2)x +y-0Row Equivalence In Exercises 55 and 56, find thereduced row-echelon matrix that is row-equivalent tothe given matrix.x+ (A - 2y - 066. (21 + 9)x - Sy -0I- Ay-02 3]ss.67. The augmented matrix represents a system of lincarequations that has been reduced using Gauss-Jordanelimination. Write a system of equations with nonzerocoefficients that the reduced matrix could represent.56. 459857. Writing Describe all possible 2x2 reducedrow-echelon matrices. Support your answer withexamples.58. Writing Describe all possible 3 x 3 reducedrow-echelon matrices. Support your answer withexamples.3 -24There are many correct answers.True or False? In Exercises 59 and 60, determine68. CAPSTONE In your own words, describe thedifference between a matrix in row-echelon formand a matrix in reduced row-echelon form. Includewhether each statement is true or false. If a statementis true, give a reason or cite an appropriate statementfrom the text. If a statement is false, provide an examplean example of cach to support your explanation.that shows the statement is not true in all cases or cite anappropriate statement from the text.59. (a) A6x 3 matrix has six rows.69. Writing Consider the ? x ? matrix :(b) Every matrix is row-equivalent to a matrix inrow-echelon form.Perform the sequence of row operations.(a) Add (-1) times the second row to the first row.(e) If the row-echelon form of the augmented matrixof a system of lincar equations contains the row(10000l, then the original system is inconsistent.(b) Add I times the first row to the second row(c) Add (-1) times the second row to the first row.(d) A homogeneous system of four lincar equations insix variables has infinitely many solutions.(d) Multiply the first row by (-1).What happened to the original matrix? Describe, ingeneral, how to interchange two rows of a matrix usingonly the second and third elementary row operations.60. (a) A 4 x 7 matrix has four columns.(b) Every matrix has a unique reduced row-echelon form.

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Description: #65 12:54Done elementary_linear_algebra_8th_edi...number of cach denomination.A System of Linear Equations In Exercises 39-42, useOa software program or a graphing utility to solve thesystem of linear equations.Matrix Representation In Exercises 49 a

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