• Support PF! Buy your school textbooks, materials and every day products Here!

Linear Algebra question

  • Thread starter Bob19
  • Start date
71
0
if one is presented with an n x n where n = 4.

What is the rule called which allows the i'th row and the j'th column to be removed from the matrix in order to make calculating the determinant easier ?

Secondly if one wants to square [tex] \left[ \begin{array}{cccc} 2 & 5 & 7 & 6 \\ 2 & 9 & 2 & 1 \\ 0 & 1 & -2 & 1 \\ 6 & 7 & 1 & -5\end{array}\right ] ^2[/tex]

Do I square every element of matrix individually ?

/Bob
 
Last edited:

Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
41,732
893
Bob19 said:
if one is presented with an n x n where n = 4.

What is the rule called which allows the i'th row and the j'th column to be removed from the matrix in order to make calculating the determinant easier ?
What you are talking about is "expansion by minors". The (n-1) x(n-1) matrix you get by removing the "i'th row and j'th column is the "minor" at that point. Choose any one row or column, calculate the minor for each element in that row or column. The determinant is the sum of the product of the element itself times its minor times either plus or minus one, depending on whether i+j is even or odd.

Secondly if one wants to square [tex] \left[ \begin{array}{cccc} 2 & 5 & 7 & 6 \\ 2 & 9 & 2 & 1 \\ 0 & 1 & -2 & 1 \\ 6 & 7 & 1 & -5\end{array}\right ] ^2[/tex]

Do I square every element of matrix individually ?

/Bob
No!! squaring a matrix means multiplying the matrix by itself, not the individual elements. You won't be able to square a matrix if you don't know how to multiply two matrices. The simplest way to remember that is to think of each row of the first matrix and each column of the second as "vectors". The i, j element of the product is the dot product of the ith row of the first matrix and the jth column of the second.
 
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
6,987
14
I think Bob may have been asking about row/column transformations to simplify the evaluation of a determinant.
 
HallsofIvy
Science Advisor
Homework Helper
41,732
893
I don't. He specifically said "which allows the i'th row and the j'th column to be removed from the matrix". That's the "expansion by minors", not "row reduction".
 

Related Threads for: Linear Algebra question

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
999
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
7
Views
1K
Top