Question

find cofactor of matrix ​

Answer 1

Answer:

एक विद्यालय में 16 लड़के हैं और उनकी औसत उम्र 25 वर्ष है। 18 तथा 19 वर्ष के दो लड़के विद्यालय छोड़कर चले जाते हैं तथा 10 और 11 वर्ष के अन्य दो लड़के उनके स्थान पर चले आते हैं तो विद्यालय के लड़कों का औसत उम्र निकालें।

Answer 2

Answer:

1. For each element, calculate the determinant of the values not on the row or column, to make the Matrix of Minor
2. Apply a checkerboard of minuses to make the Matrix of Cofactors
3. Transpose to make the Adjugate
4. Multiply by 1/Determinant to make the Inverse

Step-by-step explanation:

We can calculate the Inverse of a Matrix by:

Step 1: calculating the Matrix of Minors,

Step 2: then turn that into the Matrix of Cofactors,

Step 3: then the Adjugate, and

Step 4: multiply that by 1/Determinant.

But it is best explained by working through an example!

Example: find the Inverse of A:

It needs 4 steps. It is all simple arithmetic but there is a lot of it, so try not to make a mistake!

Step 1: Matrix of Minors

The first step is to create a "Matrix of Minors". This step has the most calculations.

For each element of the matrix:

ignore the values on the current row and column

calculate the determinant of the remaining values

Put those determinants into a matrix (the "Matrix of Minors")

Determinant

For a 2×2 matrix (2 rows and 2 columns) the determinant is easy: ad-bc

Think of a cross:

Blue means positive (+ad),

Red means negative (-bc)

 

(It gets harder for a 3×3 matrix, etc)