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Review of Linear Algebra: determinant
2022-01-15 02:11:56 【YYY speaker】
Review of linear algebra : Determinants and matrices
1. determinant : It's a value
To find a determinant is to find the value of this determinant
Two , Third order determinant : It can be used : Diagonal rule and sand method do
Diagonal rule : Subtract... From the sum of the main diagonals Sum of sub diagonal products .
a b
c d : The value is ad-bc
Be careful :n rank :n That's ok n Column .
2. If it is n How to find the order determinant ?
1. Lower triangle rule ( Above the main diagonal are 0):
The determinant is transformed into the product of the value of the lower triangular determinant equal to the value of the element of the main diagonal .
Like the upper triangle .
2. Is the determinant expansion :
Keep turning large determinants into small determinants :
determinant = Elements * Algebraic cofactor ( This line is not... Except for one element 0, Everything else is 0, It's equal to the value of this element multiplied by the algebraic cofactor of this element )
The remainder formula : Cross out the row and column of an element : Get a new determinant : This determinant is the cofactor of this element
Algebraic cofactor : Namely (-1) Of (i+j) Power * The remainder formula
Note here : Symbol
M: Denotes the remainder ( With subscript )
A: Represents the algebraic cofactor
The element of a determinant is :a
The sign of determinant :D
3. The nature of determinants :
1. A number multiplied by a determinant is equal to the number multiplied by the determinant of each element of a row or column of the determinant
2. The determinant remains unchanged : Calculate the determinant obtained by multiplying one row or column by a number and adding it to another row or column : It's the symbol
r1+r2k
c1+c2k
Problem practice 1:
To calculate the determinant : Determinant expansion
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https://chowdera.com/2021/12/202112122241266038.html
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