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.
• 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.