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VINOD A V,

PGT Mathematics,

Jawahar Navodaya Vidyalaya,

Thrissur-KERALA

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MINORS AND COFACTORS

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Minor of an element

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To each element of a matrix, a number called its minor is associated.

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The minor of an element is the value of the determinant obtained by deleting the row and column containing the element.

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Examples:

 

Remark Minor of an element of a matrix of order n (n ≥ 2) is a determinant of order n – 1.

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Cofactor of an element

 

 

 

Minors and Cofactors

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Note:-

 

 

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  • If elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero.

 

 

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ADJOINT OF A SQUARE MATRIX

 

Adjoint of a Square matrix of Order 2

 

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Adjoint of a Square matrix of Order 3

 

Example

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Theorem:

 

Proof

 

 

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Verification

 

 

 

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INVERSE OF A MATRIX

 

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Properties of Inverse

 

Hence a square matrix A is invertible if and only if A is non-singular.

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  • Every invertible matrix possesses a unique inverse

 

 

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Solution:

 

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SOLUTION OF A SIMULTANEOUS LINEAR EQUATIONS

 

 

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Solution:

 

 

Solution

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Solution:

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Q.

Two schools A and B want to award their selected teachers on the values of honesty, hard work and regularity. The school A wants to award ` x each, ` y each and ` z each for the three respective values to 3, 2 and 1 teachers with a total award money of ` 1.28 lakhs. School B wants to spend ` 1.54 lakhs to award its 4, 1 and 3 teachers on the respective values (by giving the same award money for the three values as before). If the total amount of award for one prize on each value is ` 57000, using matrices, find the award money for each value.

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According to the question,

Solution:

 

Two schools A and B want to award their selected teachers on the values of honesty, hard work and regularity. The school A wants to award ` x each, ` y each and ` z each for the three respective values to 3, 2 and 1 teachers with a total award money of ` 1.28 lakhs. School B wants to spend ` 1.54 lakhs to award its 4, 1 and 3 teachers on the respective values (by giving the same award money for the three values as before). If the total amount of award for one prize on each value is ` 57000, using matrices, find the award money for each value.

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Question:

 

 

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THANKS

Vinod A V,

JNV Thrissur