Matrix M1=[1];
Matrix M2= 2 3
( 2*2 ) 4 5
Matrix (3*3)M3 = 6 7 8
9 10 11
12 13 14
Matrix(4*4) M4= 15 16 17 18
19 20 21 22
23 24 25 26
27 28 29 30
..... etc for Matrix Mn
Find the sum of elemnts of the main diagonal. and give the solution in terms of A+Bn+Cn^2...
Hello, kamaksh_ice!
... and so on to matrix .
Find the sum of elements of the main diagonal.
We have: .
Each is the sum of an arithmetic series.
. .
In the matrix, the common difference is , and there are terms.
We must determine the first terms of these series:
After some algebra, we find that: .
The sum of an arithmetic series is: .
So we have: .
. . which simplifies to: .