Matrix Multiplication With Example

07 Jul, 2021

Divide a matrix of order of 22 recursively till we get the matrix of 22. As an example lets take a general 2 3 matrix multiplied by a 3 2 matrix.

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Multiply the elements in the first row of A with the corresponding elements in the first column of B.

Matrix multiplication with example. This gives us the answer well need to put in the first row second column of the answer matrix. E E to have a product the number of columns of left matrix B must equal the number of rows of right matrix E. Combine the result of two matrixes to find the final product or final matrix.

We add the resulting products. The first row can be selected as X. In these lessons we will learn how to perform matrix multiplication.

The first row hits the first column giving us the first entry of the product. A times B beginbmatrix 1 3 1 1 2 0 1 1 2 end bmatrix times beginbmatrix 2 6 0 1 5 1 0 1 4 end bmatrix. We will illustrate matrix multiplication or matrix product by the following example.

Since this is the case then it is okay to multiply them together. Following that we multiply the elements along the first row of matrix A with the corresponding elements down the second column of matrix B then add the results. And the element in first row first column can be selected as X.

We have many options to multiply a chain of matrices because matrix multiplication is associative. For example X 1 2 4 5 3 6 would represent a 3x2 matrix. The multiplication between matrices is done by multiplying each row of the first matrix with every column of the second matrix and then adding the results just like in the next example.

To understand the general pattern of multiplying two matrices think rows hit columns and fill up rows. Matrix E right number of rows 3. The process is shown below.

Use the previous set of formulas to carry out 22 matrix multiplication. For example if we had four matrices A B C and D we would have. Row 1 C 11 A 11 B 11 A 12 B 21 A 13 B 31 C 12 A 11 B 12 A 12 B 22 A 13 B 32.

We multiply and add the elements as follows. Notice that since this is the product of two 2 x 2 matrices number of rows and columns the result will also be a 2 x 2 matrix. ABCD AB CD A BCD.

211 -4-2 -16 18 32. Add the products to get the element C 11. The reduce step in the MapReduce Algorithm for matrix multiplication.

Find C A B. From high school calculus. Abcdefuvwxyz The answer will be a 2 2 matrix.

Since the column number of the first matrix is equal to the row number of the second matrix we can go ahead and perform the multiplication. A B C c ij k12n a ik c kj. In other words no matter how we parenthesize the product the result will be the same.

Consider the following example. Now these are the steps. We work across the 1st row of the first matrix multiplying down the 1st column of the second matrix element by element.

Matrix B left number of columns 3. The final step in the MapReduce algorithm is to produce the matrix A B. In this eight multiplication and four additions subtraction are performed.

Multiplication of two matrices X and Y is defined only if the number of columns in X is equal to the number of rows Y.

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