![]() ![]() ![]() If we have been given a chain of matrices of some arbitrary length ' n n n', the number of multiplication steps required to multiply all the matrices highly depends on the order in which we multiply them. And if the condition satisfies the resultant matrix (say P P P) will be of dimension x 1 × y 2 x_1\times y_2 x 1 × y 2 and it requires x 1 × x 2 × y 2 x_1\times x_2 \times y_2 x 1 × x 2 × y 2 multiplication steps to compute P P P. X X X and Y Y Y can be multiplied if and only if x 2 = y 1 x_2=y_1 x 2 = y 1 . Let's say we have two matrices, X X X of dimensions x 1 × x 2 x_1\times x_2 x 1 × x 2 and Y Y Y of dimensions y 1 × y 2 y_1\times y_2 y 1 × y 2 . But, multiplying two matrices is not as simple as multiplying two integers, certain rules need to be followed during multiplying two matrices. ![]() In linear algebra, matrix multiplication is an operation that produces a matrix from two matrices.
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