Matrices | Class 12 Mathematics Notes

3.4 Operations on Matrices

Matrix operations include addition, scalar multiplication, subtraction, and multiplication of matrices. Addition is defined only for matrices of the same order and involves adding corresponding elements. Scalar multiplication involves multiplying each element of a matrix by a scalar. The negative of a matrix is defined as multiplication by -1. Subtraction of matrices is defined as addition of the negative matrix. Matrix multiplication is defined when the number of columns of the first matrix equals the number of rows of the second. The product matrix has order equal to the number of rows of the first and columns of the second matrix. Each element of the product is the sum of products of corresponding elements of the row of the first and column of the second matrix. Matrix multiplication is associative and distributive but not commutative in general. The identity matrix acts as the multiplicative identity. Zero matrices can result from multiplication of non-zero matrices.

🧪 Activity: Example 11: Using matrix multiplication to calculate total sales and profit.

🔗 Connection: Leads to properties of matrix operations and transpose of matrices.