Design analysis and algorithms matrix multiplication detailed 10-marker

MATRIX CHAIN MULTIPLICATION
DEFINITION
Matrix multiplication is an operation in which
two matrices are multiplied by taking the rows
of the first matrix and the columns of the
second matrix to produce a new matrix.

Row × Column Rule
To find an element of the result matrix:
👉 Multiply elements of a row of first matrix
with corresponding elements of a column of
second matrix
👉 Then add all the products

Formula


👉 This means:
Take row i from matrix A
Take column j from matrix B
Multiply and add all corresponding
elements

, Associative but NOT Commutative
Matrix multiplication is associative, which
means:
(A*B)C = A(B*C)

👉 We can change brackets (grouping)
👉 Final result remains same
Matrix multiplication is not commutative,
which means:
AB!=BA
👉 Changing order gives different result (or
sometimes not even possible)

Explanation
In matrix multiplication, order matters, so
we cannot swap matrices
But we can change how we group them
using brackets
Different grouping may change number of
calculations, even though result remains
same