Tell me about matrices, including addition, subtraction and multiplication. |
First, matrices can only be added if they have the same number of rows and columns.
If this is the case, we say that the matrices are conformable for addition.
If the matrices are conformable, simply add the corresponding elements:
Matrices are conformable for subtraction if they have the same number of rows and columns.
Subtract the elements of the second matrix from the corresponding elements of the first:
Matrices are conformable for multiplication if the number columns in the first matrix is equal to the number of rows in the second.
NB: The order of the matrices is important for matrix multiplication.
In general, A × B is not equal to B × A.
In general a p × q matrix multiplied by a q × r matrix results in a matrix that is p × r in shape.
Split the left matrix into rows, and the right matrix into columns.
To find the top-left element of the answer matrix,
Take the top row of the first matrix,
and the left column of the second matrix.
Multiply corresponding elements, and add.
Repeat with each row/column combination to fill the entire matrix, as shown below.
Click Refresh to see the step-by-step working again
