Notes, solutions of unit 01, General Mathematics 9, for Punjab Curriculum & Textbook Board (PCTB), Lahore.

After studying this unit , the students will be able to:

  • Define
    • a matrix with real entries and relate its rectangular layout (formation) with real life,
    • rows and columns of a matrix,
    • the order of a matrix,
    • equality of two matrices.
  • Define and identify row matrix, column matrix, rectangular matrix, square matrix, zero/null matrix, diagonal matrix, scalar matrix, identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices.
  • Know whether the given matrices are suitable for addition/subtraction.
  • Add and subtract matrices.
  • Multiply a matrix by a real number.
  • Verify commutative and associative laws under addition.
  • Define additive identity of a matrix.
  • Find additive inverse of a matrix.
  • Know whether the given matrices are suitable for multiplication.
  • Multiply two (or three) matrices.
  • Verify associative law under multiplication.
  • Verify distributive laws.
  • Show with the help of an example that commutative law under multiplication does not hold in general (i.e., $AB \neq BA$).
  • Define multiplicative identity of a matrix.
  • Verify the result $(AB)^t = B^t A^t$.
  • Define the determinant of a square matrix.
  • Evaluate determinant of a matrix.
  • Define singular and non-singular matrices.
  • Define adjoint of a matrix.
  • Find multiplicative inverse of a non-singular matrix A and verify that $AA^{-1} = I = A^{-1}A$ where I is the identity matrix.
  • Use adjoint method to calculate inverse of a non-singular matrix.
  • Verify the result $(AB)^{-1} = B^{-1}A^{-1}$
  • Solve a system of two linear equations and related real life problems in two unknowns using
  • Matrix inversion method,
  • Cramer’ s rule.