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Review of Linear Algebra: determinant

2022-01-15 02:11:56 YYY speaker

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

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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+c2
k

Problem practice 1:

To calculate the determinant : Determinant expansion

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