Answered: X1 + hx2 = 3 5x, + 10x2 = k %3D

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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7. Consider the following system of linear equations: X1-X2 + 2x3 = 1 -X1 + x3 = 41+s (-2x1+x2+ rx3 = 2 1) For what values of r and s is this system of linear equations inconsistent? 2) For what values of r and s is this system of linear equations have infinitely many solutions? 3) For what values of r and s is this system of linear equations have a unique solution?
a) Find the general solution of the following system:x3+ 2x4−x5= 4,x4−x5= 3,x3+ 3x4−2x5= 7,2x1+ 4x2+x3+ 7x4= 7. b) Choosehandksuch that the system hasi) no solution,ii) a unique solution, andiii) many solutions. x1−x2=h 3x1+kx2= 5
Solve the system and write the general solution: -3x+4y+5z=1 2y - z=1 -3x+14y =6 A)The system has a unique solution. The solution set is: B) The system has infinitely many solutions. The solution set is:
Consider two real systems, say Ax = b and Cy = d. If the two systems have the samenonempty solution set, then, is it necessary that row(A) = row(C)?
a)Solve the following system of equations. Let z be the parameter. 2x+3y−z =1 3x+5y+z =4 b)For the following system of equations in echelon form, tell how many solutions there are in nonnegative integers. x+3y+z =88 7y+2z =56 c) For the following system of equations in echelon form, tell how many solutions there are in nonnegative integers. 2x+3y+2z =80 y−2z =20 d) A person has $22,000invested in stock A and stock B. Stock A currently sells for $40a share and stock B sells for $90a share. If stock B triplesin value and stock A goes up 50%, his stock will be worth $60,000. How many shares of each stock does he own?
2) Find a, b such that the following system has: xi+3x2-2x3=0 3x1+5x2-3x3 =b 3x1-2x2+ax3=0 a) Infinitely many solutions. b) Unique solution. c) No solution.
Given the linear system: a + kb − c = 22a − b + kc = 5a + 10b − 6c = 1 for which values of k has the system: 1) no solution 2) a unique solution 3) Infinitely many solutions
22. Use one solution, no solutions, or infinitely many solutions to complete each statement. a. When the solution of a system of linear equations yields the equation 4 = 4, the system has b. When the solution of a system of linear equations yields the equation x = 4, the system has c. When the solution of a system of linear equations yields the equation 0= 4, the system has HO

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