Operations with matrices (addition, subtraction, scalar multiplication)

Operations with matrices (addition, subtraction, scalar multiplication)

Understanding Matrices

  • A matrix is a rectangular array of numbers arranged in rows and columns. It is a useful mathematical tool in dealing with grouped data.

  • The size of a matrix is determined by its number of rows and columns, expressed as r x c, where r indicates the number of rows, and c shows the number of columns.

  • The position of an element in a matrix is defined by its row and column number.

Matrix Operations

Addition & Subtraction

  • Two matrices can only be added or subtracted if they are of the same size.

  • Matrix addition or subtraction is performed element-by-element. That is, to add or subtract two matrices, simply add or subtract the corresponding elements.

Scalar Multiplication

  • Scalar multiplication involves multiplying a matrix by a scalar (a single numeric value).

  • Each element in the matrix is multiplied by the scalar.

  • This operation can be applied to matrices of any size.

Performing Matrix Operations

  • When adding or subtracting matrices, ensure they have the same dimensions. Then add or subtract the corresponding elements individually.

  • For scalar multiplication, you multiply every element in the matrix by the scalar to generate a new matrix.

Understanding Matrices Operations

  • The order of matrix addition or subtraction does not matter. That is, A + B = B + A and A - B ≠ B - A.

  • Scalar multiplication is also commutative as follows: λ(A+B) = λA + λB.

  • Basic operations with matrices form the fundamentals for more complex matrix operations such as multiplication of matrices and finding inverse of a matrix.

Applications of Matrix Operations

  • Matrix operations are widely used in programming, physics, engineering and computer graphics for tasks such as transformation and manipulation of data.

  • Knowledge of matrix operations can prove useful in solving systems of linear equations in multiple variables.

  • Also, understanding matrix operations can ease the understanding of advanced topics like eigenvectors and eigenvalues.