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GATE | GATE-CS-2015 (Set 2) | Question 65

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Perform the following operations on the matrix 

⎡ 3  4   45⎤
⎢ 7  8  105⎥
⎣13  2  195⎦ 
  1. Add the third row to the second row.
  2. Subtract the third column from the first column.

The determinant of the resultant matrix is _____________.

(A)

50
 

(B)

1
 

(C)

0
 

(D)

100
 



Answer: (C)

Explanation:

The given matrix is singular matrix as its last column is a multiple of first column. If we multiply 15 with first column, we get the third column. 
Ranks is less than 3, determinant must be 0. 


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Last Updated : 08 Jan, 2019
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