NCERT Mathematics, Class 12, textbook pages 76–103 (Part I)

How to help your child with Class 12 Maths Chapter 4, Determinants, at home

Determinants, adjoint, inverse and systems, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

|3 1||2 4| = 3·4 − 1·2= 10

NCERT Class 12 Maths Chapter 4 Determinants: what it teaches

Your teen computes 2 × 3 and 3 × 3 determinants, uses them for areas of triangles, finds adjoints and inverses, and solves systems of linear equations with matrices.

Why it matters later. Determinants are used in vectors (cross product), 3D geometry and linear algebra.

See it: this chapter in pictures

A⁻¹ = adj A / |A||A| = 0 → no inversesingular matrix
Check the determinant first.
x + y = 5, 2x − y = 1X = A⁻¹Bx = 2, y = 3
Matrix method for equations.
triangle (1,0), (6,0), (4,3)area = ½ |det|= 7.5
Determinants measure area.

You need

  • a calculator
  • practice systems of equations

Tonight’s 60 minutes

  1. Find det [[3, 1],[2, 4]] (10).
  2. Expand a 3 × 3 determinant along a row.
  3. Find the area of a triangle with vertices (1, 0), (6, 0), (4, 3) (7.5).
  4. Solve x + y = 5, 2x − y = 1 using A⁻¹B (2, 3).

Words to use

  • determinant
  • minor
  • cofactor
  • adjoint
  • inverse
  • singular

Watch for

  • Sign errors in cofactors. Use the checkerboard + − + pattern.
  • Trying to invert a singular matrix. If det = 0, no inverse exists.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

Youdet [[3,1],[2,4]]?

Your child3·4 − 1·2 = 10.

A game for this week: Inverse check

  1. Pick a 2 × 2 matrix.
  2. Find its inverse.
  3. Multiply to check you get I.
  4. Swap matrices.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Solving circuits.
  • Computer graphics.
  • Economics models.
  • Cryptography.

Quick check

Ask these at the end of the week. Tap to see the answer.

det [[3, 1],[2, 4]]?

10.

If det A = 0, is A invertible?

No.

Solution of x + y = 5, 2x − y = 1?

x = 2, y = 3.

Ready for the next chapter when your child…

  • Computes determinants.
  • Finds adjoint and inverse.
  • Solves systems with matrices.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

What does det = 0 mean?

The matrix is singular and has no inverse.

How do I find an inverse?

A⁻¹ = adj A / det A.

How are determinants used for area?

Half the absolute determinant of the coordinates gives a triangle’s area.