Scribd
Upload
152 views2 pages

Practice Questions On Matrices 2

The document contains 10 practice questions on matrices. Question 1 asks to find the rank of two matrices by reducing them to row-echelon form. Question 2 asks to reduce two matrices to normal form and find their ranks. Question 3 asks to find non-singular matrices P and Q such that PAQ is in normal form for two given matrices. Question 4 asks to solve four systems of linear equations. Question 5 asks whether two sets of vectors are linearly dependent or independent. Question 6 tests three systems of equations for consistency. Question 7 asks to find values of λ for which a system of equations is consistent. Questions 8 and 9 ask to solve systems of equations using Gauss elimination and Gauss-Jordan methods. Question 10 asks

Uploaded by

Dev Sawant
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
152 views2 pages

Practice Questions On Matrices 2

The document contains 10 practice questions on matrices. Question 1 asks to find the rank of two matrices by reducing them to row-echelon form. Question 2 asks to reduce two matrices to normal form and find their ranks. Question 3 asks to find non-singular matrices P and Q such that PAQ is in normal form for two given matrices. Question 4 asks to solve four systems of linear equations. Question 5 asks whether two sets of vectors are linearly dependent or independent. Question 6 tests three systems of equations for consistency. Question 7 asks to find values of λ for which a system of equations is consistent. Questions 8 and 9 ask to solve systems of equations using Gauss elimination and Gauss-Jordan methods. Question 10 asks

Uploaded by

Dev Sawant
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 2

Practice questions on Matrices

1) Find the rank of the matrix using Row-echelon form of


following matrix.
6 1 3 6
2 3 1 4   
 
i) A  5 2 3 0 ii) A
10
4 2 6 1
3 9 7
9 8 0 8  
 
16 4 12 13

2) Reduce the matrix to normal form and find it’s rank


1 1 2 3
1 1 0   
 
i) A   2 2 0 ii) A
4 1
0 3
0 2
1 4
 0 1 0  
 
0 1 0 2

3) Find the non-singular matrix P and Q such that PAQ is in normal form,
1 2 3 4  1 1 1 
i) A  2 1 4 3  ii) A  1  1  1
3 0 5  10 3 1 1 
  

4) Solve the following equations


i) x+2y+3z=0; 2x+3y+z=0; 4x+5y+4z=0; x+2y-2z=0
ii) x+y+2z=0; x+3y+4z=0; x+2y+3z=0; 3x+4y+7z=0
iii) 2x-y+3z=0; 3x+2y+z=0; x-4y+5z=0
iv) 3x+y-5z=0; 5x+3y-6z=0; x+y-2z=0; x-5y+z=0

5) Examine whether the following vectors are linearly dependent or


independent
i) [2,1,1] , [1,3,1], [1,2,-1] ii) [3,1,-4], [2,2,-3], [0,-4,1]

6) Test the following equations for consistency


i) x+2y-z=1; x+y+2z=9; 2x+y-z=2
ii) x-3y-3z=-10; 3x+y-4z=0; 2x+5y+6z=13
iii) 6x+y+z=-4; 2x-3y-z=0; -x-7y-2z=7

7) Find the values of λ for which the system of equations x+y+4z=1;


X+2y-2z=1; λx+y+z=1.

8) Solve the following equations by Gauss elimination method;


i) x+y+z=2; 2x+2y-z=1; 3x+4y+z=9
ii) 2x+y+z=10; 3x+2y+3z=18; x+4y+9z=16
9) Solve the following equations by Gauss-Jorden method,
i) 3x+2y-2z=4; x-2y+3z=6; 2x+3y+4z=15
ii) X+2y+z=8; 2x+3y+4z=20; 4x+3y+2x=16

10) Solve the equations by using Gauss-Seidel method,


i) 15x+y+z=17; 2x+15y+z=18; x+2y+15z=18
ii) 10x+2y+z=9; 2x+20x-2z=-44; -2x+3y+10z=22

You might also like