Matrices - Addition And Substraction Of Matrices

Addition and Subtraction of Matrices

Definition, Properties, and Applications

Matrix addition and subtraction involve combining or removing corresponding elements from two matrices of the same order. These operations are performed element-wise.

Key Formula

\[ A \pm B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \pm \begin{pmatrix} x & y \\ z & u \end{pmatrix} = \begin{pmatrix} a \pm x & b \pm y \\ c \pm z & d \pm u \end{pmatrix} \]

This formula shows that matrices can be added or subtracted by performing the operation on each corresponding element, provided both matrices have the same dimensions.

Terminology

  • Matrix: A grid of numbers arranged in rows and columns.
  • Order: The size of the matrix defined by the number of rows and columns (e.g., 2×2).
  • Element-wise Operation: Operation applied to each pair of corresponding elements.
  • Conformable Matrices: Matrices that have the same dimensions, allowing them to be added or subtracted.

Applications

  • Used in image processing for combining or altering pixel matrices.
  • Common in physics and engineering simulations where multiple sets of data are combined.
  • Helps in solving systems of linear equations and in matrix-based algorithms.
  • Used in financial modeling to compute changes in data tables over time.
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