Maths - Matrix algebra - 3D arithmatic

The following calculator allows you to calculate 3x3 matrix arithmetic. Enter the values into the matrix into the top two matries and then press "+ - or * " to display the result in the bottom matrix:

 

 

=

Matrix Addition

To add matrices just add the corresponding elements, so for 3x3 matrices and then,

a00 + b00 a01 + b01 a02 + b02
a10 + b10 a11 + b11 a12 + b12
a20 + b20 a21 + b21 a22 + b22
=
a00 a01 a02
a10 a11 a12
a20 a21 a22
+
b00 b01 b02
b10 b11 b12
b20 b21 b22

Matrix Subtraction

To subtract matrices just subtract the corresponding elements, so for 3x3 matrices and then,

a00 - b00 a01 - b01 a02 - b02
a10 - b10 a11 - b11 a12 - b12
a20 - b20 a21 - b21 a22 - b22
=
a00 a01 a02
a10 a11 a12
a20 a21 a22
-
b00 b01 b02
b10 b11 b12
b20 b21 b22

Matrix Multiplication

The multiplication of two 3x3 matrices is:

a00*b00 + a01*b10 + a02*b20 a00*b01 + a01*b11 + a02*b21 a00*b02 + a01*b12 + a02*b22
a10*b00+ a11*b10 + a12*b20 a10*b01 + a11*b11 + a12*b21 a10*b02 + a11*b12 + a12*b22
a20*b00 + a21*b10 + a22*b20 a20*b01 + a21*b11 + a22*b21 a20*b02 + a21*b12 + a22*b22
=
a00 a01 a02
a10 a11 a12
a20 a21 a22
b00 b01 b02
b10 b11 b12
b20 b21 b22

This is worked out as follows: for each entry in the matrix we take the row from the first operand and the column from the second operand:

a00 a01 a02
a10 a11 a12
a20 a21 a22
b00 b01 b02
b10 b11 b12
b20 b21 b22
=
a00 a01 a02
b00
b10
b20
a00 a01 a02
b01
b11
b21
a00 a01 a02
b02
b12
b22
a10 a11 a12
b00
b10
b20
a10 a11 a12
b01
b11
b21
a10 a11 a12
b02
b12
b22
a20 a21 a22
b00
b10
b20
a20 a21 a22
b01
b11
b21
a20 a21 a22
b02
b12
b22

This single row times a single column is equivalent to the dot product.


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