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 |
|
= |
|
This single row times a single column is equivalent to the dot product.
This site may have errors. Don't use for critical systems.
