To be added together, two matrices must have the same number of rows and columns. Two 3x3 matrices can be added together, but a 3x3 matrix and a 4x3 matrix cannot because they have a different number of columns. To add matrices, add together the numbers in the corresponding positions to create a new matrix.
One matrix can only be subtracted from another if the two matrices have the same number of rows and columns. To subtract matrices, subtract the numbers in corresponding positions, and use the results to create a new matrix.
A single number that is multiplied with a matrix is called a scalar. To multiply a matrix by a scalar, multiply each number of the matrix by the scalar. The resulting numbers create the new matrix.
To multiply two matrices together, the number of columns in the first matrix must equal the number of rows in the second matrix. To calculate the first number of the resulting matrix, multiply the first number of the first row of the first matrix by the first number in the first column of the second matrix. Then multiply the second number in the row by the second number of the column, followed by the third, fourth, fifth, etc. When the products of the multiplication are added together they become the first number of the new matrix. Follow the same steps for the additional rows and columns to calculate the other numbers in the new matrix. The new matrix has the same number of rows as the first matrix and the same number of columns as the second matrix.Learn more about Algebra