Q1. Using Gauss elimination method solve the system of simultaneous linear equations (1) 5x + 2y = -1 3x-2y = -7 3z-Gy 9 (2) (3) 1 3r-6y -2x+4y= -6' Michal Sawa (michal.sawa@wab.edu.pl) -1 (4) 3r-y-2:- -1 5x+3y-4- -3 Q2. Using Gauss elimination method solve the system of simultaneous linear equations z-y+-28+ = 0 (1) 3x+4y-2+8+3t = 1 2-8y +52-98+1= [1 2 0 (2) B-2 30 1-1 1 x+2y-1 (5) -x-3y += = 0. 2x+3y-2: -5 Q3. For what values of the parameter k the system of equations has one (unique) solution? Discuss the number of solutions in the remaining cases. (1) kx+y=A² Q7. Find all matrices that commute with A- z+2y+z+1=7 (2) 5z + 5y +2:+7= 1 2x-y-+42 Q4. Using elementary transformations of augmented matrix [M] to (M-¹] find inverse matrix to (1) A- 1 2004 0001 0 200 0 -1 0 1 z+k²y+z=-k (2) z+y-ka-k² (3) C- Q5. Find ranks of the matrices [202 (1) A-2 0 2 311 Q6. Using Rouché-Capelli theorem discuss consistency of the system of equations 3r+2y = 1 4x+3y-2-2. -2x-y+: 0 Determine the dimension of the space of solutions (the number of degrees of freedom). -3) (2) B- 4 2 02 ie, such matrices B that AB BA.

Q1. Using Gauss elimination method solve the system of simultaneous linear equations (1) 5x + 2y = -1 3x-2y = -7 3z-Gy 9 (2) (3) 1 3r-6y -2x+4y= -6' Michal Sawa (michal.sawa@wab.edu.pl) -1 (4) 3r-y-2:- -1 5x+3y-4- -3 Q2. Using Gauss elimination method solve the system of simultaneous linear equations z-y+-28+ = 0 (1) 3x+4y-2+8+3t = 1 2-8y +52-98+1= [1 2 0 (2) B-2 30 1-1 1 x+2y-1 (5) -x-3y += = 0. 2x+3y-2: -5 Q3. For what values of the parameter k the system of equations has one (unique) solution? Discuss the number of solutions in the remaining cases. (1) kx+y=A² Q7. Find all matrices that commute with A- z+2y+z+1=7 (2) 5z + 5y +2:+7= 1 2x-y-+42 Q4. Using elementary transformations of augmented matrix [M] to (M-¹] find inverse matrix to (1) A- 1 2004 0001 0 200 0 -1 0 1 z+k²y+z=-k (2) z+y-ka-k² (3) C- Q5. Find ranks of the matrices [202 (1) A-2 0 2 311 Q6. Using Rouché-Capelli theorem discuss consistency of the system of equations 3r+2y = 1 4x+3y-2-2. -2x-y+: 0 Determine the dimension of the space of solutions (the number of degrees of freedom). -3) (2) B- 4 2 02 ie, such matrices B that AB BA.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 17EQ

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