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.

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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Question

13:29
(3)
Q1. Using Gauss elimination method solve the system of simultaneous linear equations
5x + 2y = -1
(1) 3r-2y = -7'
(4)
x+2y = -1
3r-y-2: = -1
5x+3y-4: -3
-9
(2)
-2x + 4y
Linear Algebra & Analytic Geometry - Set 4.
3z-6y=
1
3r-6y
-2x + 4y = -6
LA_AG_Set_4
Q2. Using Gauss elimination method solve the system of simultaneous linear equations
z-y+z-28+0
(1) 3x+4y-2+8+3= 1
2-8y +52-98+1=-1
Q5. Find ranks of the matrices
[202
2 0 2 2
31 1 2
(1) A
Michal Sawa (michal.sawa@wab.edu.pl)
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.
z+ky 1
(1) kr+y=k²
z+2y+=+ = 7
(2) 5z + 5y +2:+ 7 = 1
2z-y-z+4t 2
Q4. Using elementary transformations of augmented matrix [M] to [IM-¹] find inverse matrix to
(1) A1
-3 5
[1 2 0]
(2) B-2 30
-1 1
2 004
0001
0 200
-1 0 1 0
Q7. Find all matrices that commute with A=
z+k²y+z= -k
(2) x+y-kz- k²
y+ 1
(3) C-
4
(2) B 1 2
021
Q6. Using Rouché-Capelli theorem discuss consistency of the system of equations
....
3x +2y = 1
4x+3y
= 2.
-2z-y +z = 0
Determine the dimension of the space of solutions (the number of degrees of freedom).
i.e. such matrices B that AB = BA.

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