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21 + 2x2 - 3rs = -2 4. Find the value of k for which the system of equations 3r1 - *2 - 2x3 2r + 3r2 - 5x3 = k - 1 is consistent

21 + 2x2 - 3rs = -2 4. Find the value of k for which the system of equations 3r1 - *2 - 2x3 2r + 3r2 - 5x3 = k - 1 is consistent

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(b) Gauss-Jordan method. (c) Cramer's Rule. E. Okyere Page 1 of 3 MATH 209: LINEAR ALGEBRA FOR ENGINEERS Ii + 2x2 - 3rs = -2 4. Find the value of k for which the system of equations 3r1 - 12 - 2.r3 = 1 2x1 + 3r2 - 5x3 = k is consistent 21 + x2+ 13 = 1 5. Find the value of k for which the system of equations 3x1 - 12 - 13 = 4 is inconsistent 21 + 5r2 + 5x3 = k 2x1 - 3r2 + r3 = 0 6. Find the value of k for which the system of equations rı + 2x2 - 3r3 = 0 has non trivial 4x, - x2+ kra = 0 solutions. 7. Use the Gaussian elimination method to find the solution set of the following systems and that of their associated homogeneous forms. x1 + 2x2 - r3 = 1 a) 2x1 + 4x2 = 2 3r2 - 5x3 3 I1 - r2 + 3 = 1 b) 3r1 5x1 - 2r2 + 3r3 = 5 + r3 = 3 8. Suppose that the augmented matrix corresponding to some linear system Ax = b reduces to the following: 1 2 0 0 7 0 0|18 0 0 10 4 0 0 0 0 0 1 -3 0 0 0 0 0 0 0 0 1p 0 0 0 0 0 0 0 k (a) Using your own unknown variables for the given reduced system, identify the basic and free variables. (b) What conditions (if any) are there on r, p, k so that (i) there are no solutions to Ax = b (ii) there is exactly one solution to Ax = b (iii) there are infinitely many solutions to Ax = b 9. Consider the matrix -1 A = -4 k 4 -2 (a) If A is the augmented matrix of a system of linear equations, determine the number of equations and the number of variables. E. Okyere Page 2 of 3 MATH 209: LINEAR ALGEBRA FOR ENGINEERS (b) If A is the augmented matrix of a system of linear equations, find the value(s) of k such that the system is consistent. 10. If a 7 x 7 matrix A has det (A) = 1/4, compute the following determinants: (a) det(5A) (b) det(-3A) (c) det(A*) (d) det(A-)
Transcribed Image Text:(b) Gauss-Jordan method. (c) Cramer's Rule. E. Okyere Page 1 of 3 MATH 209: LINEAR ALGEBRA FOR ENGINEERS Ii + 2x2 - 3rs = -2 4. Find the value of k for which the system of equations 3r1 - 12 - 2.r3 = 1 2x1 + 3r2 - 5x3 = k is consistent 21 + x2+ 13 = 1 5. Find the value of k for which the system of equations 3x1 - 12 - 13 = 4 is inconsistent 21 + 5r2 + 5x3 = k 2x1 - 3r2 + r3 = 0 6. Find the value of k for which the system of equations rı + 2x2 - 3r3 = 0 has non trivial 4x, - x2+ kra = 0 solutions. 7. Use the Gaussian elimination method to find the solution set of the following systems and that of their associated homogeneous forms. x1 + 2x2 - r3 = 1 a) 2x1 + 4x2 = 2 3r2 - 5x3 3 I1 - r2 + 3 = 1 b) 3r1 5x1 - 2r2 + 3r3 = 5 + r3 = 3 8. Suppose that the augmented matrix corresponding to some linear system Ax = b reduces to the following: 1 2 0 0 7 0 0|18 0 0 10 4 0 0 0 0 0 1 -3 0 0 0 0 0 0 0 0 1p 0 0 0 0 0 0 0 k (a) Using your own unknown variables for the given reduced system, identify the basic and free variables. (b) What conditions (if any) are there on r, p, k so that (i) there are no solutions to Ax = b (ii) there is exactly one solution to Ax = b (iii) there are infinitely many solutions to Ax = b 9. Consider the matrix -1 A = -4 k 4 -2 (a) If A is the augmented matrix of a system of linear equations, determine the number of equations and the number of variables. E. Okyere Page 2 of 3 MATH 209: LINEAR ALGEBRA FOR ENGINEERS (b) If A is the augmented matrix of a system of linear equations, find the value(s) of k such that the system is consistent. 10. If a 7 x 7 matrix A has det (A) = 1/4, compute the following determinants: (a) det(5A) (b) det(-3A) (c) det(A*) (d) det(A-)
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