Open In App
Related Articles

GATE | GATE CS 2013 | Question 3

Improve
Improve
Improve
Like Article
Like
Save Article
Save
Report issue
Report

Which one of the following does NOT equal to 

gatecs20132

gatecs2013

(A)

C
 

(B)

D
 

(C)

B
 

(D)

A
 



Answer: (D)

Explanation:

First of all, you should know the basic properties of determinants before approaching 
For these kind of problems. 
1) Applying any row or column transformation does not change the determinant 
2) If you interchange any two rows, sign of the determinant will change

A = | 1  x  x^2 | 
       | 1  y  y^2 | 
       | 1  z  z^2 |

To prove option (b)

=> Apply column transformation C2 -> C2+C1

C3 -> C3+C1

=> det(A) = | 1  x+1  x^2+1 | 
                     | 1  y+1  y^2+1 | 
                     | 1  z+1  z^2+1 |

To prove option (c),

=> Apply row transformations R1 -> R1-R2

R2 -> R2-R3

=> det(A) = | 0   x-y   x^2-y^2 | 
                     | 0   y-z   y^2-z^2 | 
                     | 1      z          z^2   |

To prove option (d), 

=> Apply row transformations R1 -> R1+R2

R2 -> R2+R3

=> det(A) = | 2  x+y   x^2+y^2 | 
                     | 2  y+z   y^2+z^2 | 
                     | 1     z        z^2     |



Quiz of this Question
Please comment below if you find anything wrong in the above post

Last Updated : 28 Jun, 2021
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads