Login

Articles

MORE ABOUT MATRICES

Print

moreaboutmatrices1


Under this section, we will be learning about important terms which are frequently used in matrices.

We will discuss the following:
•    Transpose of a Matrix
•    Minors
•    Co-factors

Let’s study each one in detail.



Transpose of a Matrix

Let A be a m x n matrix, then its transpose is obtained by interchanging rows into columns.  It is denoted by AT or A’
If A is of order m x n, then the order of A’ is n x m
For example:  moreaboutmatrices2      Order of A=2x3
                   

  moreaboutmatrices3    Order of A’=3x2
 

Properties of transpose of the Matrix


For any matrices A and B of suitable orders, we have
1) (A’)’= A
2) (kA)’ = kA’
3) (A + B)’ = A’ + B’
4) (AB)’ = B’A’

Let’s try the following examples:
1) If A= [1   4    5] then show that (A’)’ = A

              moreaboutmatrices4
                      
                      
                       
From (i) and (ii), we get, (A + B)’ = A’ + B’
                                     

Minor of an element


Minor of an element aij of a determinant is the determinant obtained by deleting its ith row and jth column in which aij lies.  It is denoted by Mij
Minor of an element of a determinant of order n (n ≥ 2) is a determinant of order n - 1
Example: Find the minor of the element 3 in the determinant
moreaboutmatrices5
Solution: The element 3 lies in first row and third column, so it is denoted by M13 and is given by moreaboutmatrices6
                                                 [Deleting 1st row and 3rd column]
                                    = 0 – (-15)
                                    = 15                  

Co-factor of an element


Co-factor of an element aij denoted by Aij is defined by Aij = (-1)i+j Mij ,  where Mij is the minor of aij.
Example: Find the co-factor of element -5 in the determinant moreaboutmatrices7
                                                                                              
                                                                                               
Solution: -5 belongs to 3rd row and 1st column, so it is denoted by
moreaboutmatrices8
          
      = + (0 - 15)
      = -15
                                     

Now try it yourself!  Should you still need any help, click here to schedule live online session with e Tutor!

About eAge Tutoring:

eAgeTutor.com is the premium online tutoring provider.  Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.  

Contact us today to learn more about our tutoring programs and discuss how we can help make the dreams of the student in your life come true!

Reference Links:

    

Archives

Blog Subscription