What is the minimum number of multiplications required to multiply the matrices?

(i) The minimum number of multiplications required to multiply two 2 X 2 matrices is seven. (ii) The minimum number of multiplications/divisions required to multiply two complex numbers is three.

How do you find the number of matrix multiplication?

To multiply a matrix by a single number is easy:

1. These are the calculations: 2×4=8. 2×0=0.
2. The “Dot Product” is where we multiply matching members, then sum up: (1, 2, 3) • (7, 9, 11) = 1×7 + 2×9 + 3×11. = 58.
3. (1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12. = 64.
4. DONE! Why Do It This Way?

What is the minimum number of scalar multiplications required for Parenthesization?

The number of scalar multiplications required in the following sequence of matrices will be : A1((A2A3)A4) = (5 x 20 x 10) + (5 x 10 x 5) + (10 x 5 x 5) = 1000 + 250 + 250 = 1500. All other parenthesized options will require number of multiplications more than 1500.

How many multiplications are needed for matrix multiplication?

Altogether, the textbook method for multiplying two-by-two matrices requires eight multiplications, plus some additions. Generally, this way of multiplying two n-by-n matrices together requires n3 multiplications along the way.

How many operations are needed for matrix multiplication?

The obvious way to multiply two n × n matrices takes n³ operations: each entry in the product is the inner product of a row from the first matrix and a column from the second matrix. That amounts to n² inner products, each requiring n multiplications.

Where is matrix multiplication used?

Matrix multiplication is probably the most important matrix operation. It is used widely in such areas as network theory, solution of linear systems of equations, transformation of co-ordinate systems, and population modeling, to name but a very few.

How does Matrix chain multiplication work?

Matrix chain multiplication (or the matrix chain ordering problem) is an optimization problem concerning the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved.