Algebra

A matrix is a rectangular array

A matrix is a rectangular array of numbers arranged in rows and columns. Types include rectangular, square, row, column, diagonal, scalar, identity, z

Addition and subtraction require matrices

Addition and subtraction require matrices of same order, performed element-wise. Scalar multiplication multiplies each element by the scalar. Matrix m

The transpose A' of matrix

The transpose A' of matrix A is obtained by interchanging rows and columns. Properties include (A')' = A, (A+B)' = A'+B', and (AB)' = B'A'.

A symmetric matrix satisfies A' =

A symmetric matrix satisfies A' = A (diagonal elements remain same, off-diagonal elements are mirror images). A skew-symmetric matrix satisfies A' = -

For a square matrix

For a square matrix, determinant is a scalar value calculated using elements, minors, and cofactors. For 2×2: |A| = ad-bc. For 3×3: expand using any r