Questions
Syllabus
Notes
Qns. By Syllabus

Semester

Subject

💡 Jump to Important Questions ↓

Linear Equations in Linear Algebra

Preparing your PDF

Loading PDF viewer...

Previous
No previous note
Facilitator:StudyNp
Created by:
Roshan Bist

Important Questions

Important Questions

Linear Equations in Linear Algebra

Asked in 2080.1Long Question10 Marks
1.
What is a system of linear equations? When the system is consistent? Find the condition on g, h, k that makes the system consistent.
x1−4x2+7x3=gx_1 - 4x_2 + 7x_3 = g
3x2−5x3=h3x_2 - 5x_3 = h
−2x1+5x2−9x3=k-2x_1 + 5x_2 - 9x_3 = k
[10]
Asked in 2080Long Question10 Marks
2.
Define system of linear equations. When a system of equations is consistent? Make echelon form to solve:
−2a−3b+4c=5-2a - 3b + 4c = 5
b−2c=4b - 2c = 4
a+3b−c=2a + 3b - c = 2
[10]
Asked in 2079Short Question5 Marks
3.
When a linear system of equation is consistent? Find the values of h and k for which the system is consistent:
2x1−x2=h2x_1 - x_2 = h
−6x1+3x2=k-6x_1 + 3x_2 = k
[5]
Asked in 2079Long Question10 Marks
4.
Reduce the system of equations into echelon form and solve:
x1−2x2−x3+3x4=0x_1 - 2x_2 - x_3 + 3x_4 = 0
−2x1+4x2+5x3−5x4=3-2x_1 + 4x_2 + 5x_3 - 5x_4 = 3
3x1−6x2−6x3+8x4=23x_1 - 6x_2 - 6x_3 + 8x_4 = 2
[10]
Asked in 2078Long Question10 Marks
5.
Define system of linear equations. When a system of equation is consistent? Determine if the system is consistent:
−2x1−3x2+4x3=5-2x_1 - 3x_2 + 4x_3 = 5
x2−2x3=4x_2 - 2x_3 = 4
x1+3x2−x3=2x_1 + 3x_2 - x_3 = 2
[10]
Asked in 2076Long Question10 Marks
6.
When a system of linear equation is consistent and inconsistent? Give an example for each. Test the consistency and solve:
x−2y=5x - 2y = 5
−x+y+5z=2-x + y + 5z = 2
y+z=0y + z = 0
[10]
Asked in 2075Long Question10 Marks
7.
When a system of linear equation is consistent and inconsistent? Give an example for each. Test the consistency and solve:
x+y+z=4x + y + z = 4
x+2y+2z=2x + 2y + 2z = 2
2x+2y+z=52x + 2y + z = 5
[10]