Determinants Matrices Question 100
Question: If $ A={{[a _{ij}]} _{n\times n}} $ be a diagonal matrix with diagonal element all different and $ B={{[b _{ij}]} _{n\times n}} $ be some another matrix. Let $ AB={{[cij]} _{n\times n}} $ then $ c _{ij} $ is equal to
Options:
A) $ a _{jj}b _{ij} $
B) $ a _{ii}b _{ij} $
C) $ a _{ij}b _{ij} $
D) $ a _{ij}b _{ji} $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ c _{ij}=\sum\limits _{k=1}^{n}{a _{ik}b _{kj}} $
(In general) and in a diagonal matrix non-diagonal elements are zero i.e., $ a _{ij}= \begin{matrix} 0 & ifi\ne j \\ a{ & _{ii}}, & ifi=j \\ \end{matrix} . $ So, $ c _{ij}=a _{ii}b _{ij} $
BETA
