logo

Ask Questions, Get Answers

X
 
Home  >>  CBSE XII  >>  Math  >>  Matrices

If A and B are square matrices of the same order,then $(iii)\quad [k(A-B)']=\text{________}.$

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

1 Answer

Toolbox:
  • If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
Given
If A and B are square matrices of the same order then
$[k(A-B)']=k(A'-B')$
Proof:
Let A=$[a_{ij}]$
A'= $[a_{ji}]$
B=$[b_{ij}]$
B'= $[b_{ji}]$
(A-B)=$[a_{ij}$ - $b_{ij}]$
Then (A-B)'= $[a_{ji}$ - $b_{ji}]$
A'-B' = $[a_{ji}$ - $b_{ji}]$
The scalar multiplication $cA$ of a matrix $A$ and a number $c$ (also called a scalar in the parlance of abstract algebra) is given by multiplying every entry of $A$ by $c$.
Hence
$[k(A-B)']=k(A'-B')$
answered Apr 4, 2013 by sharmaaparna1
 
Download clay6 mobile appDownload clay6 mobile app
...
X