Maths - Matrix algebra - 2D arithmatic

The following calculator allows you to calculate 2x2 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, for 2x2 matrices and then,

a00 + b00 a01 + b01
a10 + b10 a11 + b11
=
a00 a01
a10 a11
+
b00 b01
b10 b11

Matrix Subtraction

To subtract matrices just subtract the corresponding elements, for 2x2 matrices and then,

a00 - b00 a01 - b01
a10 - b10 a11 - b11
=
a00 a01
a10 a11
-
b00 b01
b10 b11

Matrix Multiplication

For 2x2 matrices then,

a00*b00 + a01*b10 a00*b01 + a01*b11
a10*b00+ a11*b10 a10*b01 + a11*b11
=
a00 a01
a10 a11
b00 b01
b10 b11

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
a10 a11
b00 b01
b10 b11
=
a00 a01
b00
b10
a00 a01
b01
b11
a10 a11
b00
b10
a10 a11
b01
b11

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

a00 a01
a10 a11
b00 b01
b10 b11
=
a00*b00 + a01*b10 a00*b01 + a01*b11
a10*b00 + a11*b10 a10*b01 + a11*b11

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