MATRIX MULTIPLICATION

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Scalar Multiplication Multiplication of two matrices

Scalar Multiplication

3 4

2 6

C

Scalar Multiplication To Multiply 4C

1. First, you are going to take the scalar “4” and distribute it to each of the entries in the nxm matrix (n rows, m columns). In this case we are given a 2x2 matrix.

2. Second, you are going to take your scalar “4” and multiply it by those entries.

3. The resulting matrix will be the “4C” nxm matrix.

Multiplication of two matrices

2 1

6 2

B1 3

5 7

A

Find A B

Multiplication of two matricesWhen multiplying two matrices A and B, we must first identify the dimensions of matrix A and matrix B. Given that matrix A has dimensions nxm and matrix B has dimensions pxq, if m and p are not equal to each other, matrix multiplication cannot be done. Also note that if m and p are equal to each other, the “solution” matrix will have dimensions nxq.Doing matrix multiplication involves a process of multiplying entries in the rows of the first matrix with corresponding entries in the columns of the second matrix. We take the sum of the products and put them in the corresponding nth row, qth column.

Multiplication of two matrices

For example, given matrix A and B (we must first check that the number of columns on A equals the number of rows on B) then, we start on the first row of matrix A and the first column in matrix B.

We multiply the first entry in the first row of matrix A with the first entry in the first column of matrix B (keeping note of this product).

We then proceed to the second entry of the first row of matrix A with the second entry in the first column of matrix B. We multiply these two entries together (keeping note of this product as well).

Multiplication of two matrices

Once we have reached the final entry in the first row of matrix A with the final entry of the first column of matrix B (and took the product of those entries), you are going to add all of those products together and put this sum in the first row, first column of matrix C, (the “solution” matrix) which will be a 2x3 matrix.

Continue to stay on row 1, but proceed to column 2 of matrix B. You will repeat the previous process, multiplying the first entry in row 1 with the first entry in column 2, take that product and add it with the product of the 3 in row 1 with (-3) in column 2.

Multiplication of two matrices

Continue to stay on the first row and proceed to the next column of matrix B (following the same process to obtain the entries in C) until you have finished with the final column in matrix B.

Once you have reached the final column and filled all the entries in row 1 of the solution matrix, proceed to the next row, following the same process.

Continue this process until you have filled in all the entries of matrix C.

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