Determinants Matrices Question 136
Question: If the least number of zeroes in a lower triangular matrix is 10, then what is the order of the matrix-
Options:
A) $ 3\times 3 $
B) $ 4\times 4 $
C) $ 5\times 5 $
D) $ 10\times 10 $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Number of zeroes in a lower triangular matrix of order $ n\times n $ is $ 1+2+3+….+n=\frac{n(n+1)}{2} $ Number of zeroes = 10
$ \Rightarrow \frac{n(n+1)}{2}=10 $
$ \Rightarrow n^{2}+n=20=0 $
$ \Rightarrow (n+5)(n-4)=0 $
$ \Rightarrow n=4 $ or $ -5 $ (-5 is meaningless)
$ \Rightarrow n=4.\Rightarrow $ order of the matrix is $ 4\times 4 $
BETA
