How to multiply a 3*3 matrix ?

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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I assume you mean how to multiply a 3x3 matrix with another 3x3 matrix.

Lets use the two matrices:

A =    (a1  a12  a13; a21  a22  a23; a31  a32  a33) 

i.e., the rows are (a11  a12  a13); (a21  a22  a23) and (a31  a32  a33)


B = (b11  b12  b13; b21  b22  b23; b31  b32  b33)

where the rows are (b11  b12  b13); (b21   b22   b23) and (b31  b32  b33)

The resultant matrix of product of these two 3x3 matrices will also be a 3x3 matrix, X with rows (x11  x12  x13); (x21  x22  x23) and (x31  x32  x33)

Here x11 = a11xb11  + a12xb21 + a13xb31;

x12 = a11xb12 + a12xb22 + a13xb32.........and so on

x33 = a31xb13 + a32xb23 + a33xb33.

that is how one can calculate the product of a 3x3 matrix with another 3x3 matrix. 

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