JEE Main Matrices and Determinants: A Weekly Plan for Dwarka
This post lists the question types that repeat in JEE Main from matrices and determinants.
It also gives a weekly routine you can follow at home, with or without a tutor.
Why this chapter troubles Class 12 students
A matrix is a rectangular arrangement of numbers in rows and columns. A determinant is a single number worked out from a square matrix. The two ideas look alike on paper, but they behave differently. Many students mix them up under exam pressure.
These are the usual pain points for Class 12 students in Dwarka and nearby Gurugram sectors:
- Sign errors. A 3×3 determinant has alternating plus and minus signs. One missed sign ruins the whole answer.
- Treating matrices like numbers. Matrix multiplication is not commutative. That means AB is usually not equal to BA.
- Memorising without understanding. The student remembers a formula but cannot tell when to use it.
- Long calculations. Students expand a determinant fully when a row operation would have made it simple.
This chapter is part of the Class 12 NCERT syllabus, so school preparation and JEE Main preparation overlap here. Use that overlap. Solve the NCERT examples and exercises first. Then move to harder JEE-style questions.
Common JEE Main question types
The table below groups the question types that appear again and again. Use it as a checklist. Tick a row only when your child can solve three different questions of that type without help.
| Question type | What the student must know | Common slip |
|---|---|---|
| Determinant with variables | Row and column operations; taking out a common factor | Forgetting that swapping two rows changes the sign |
| Adjoint and inverse | Inverse of A = adj(A) divided by det(A); it exists only when det(A) is not zero | Writing the cofactors in the wrong positions |
| Properties of adjoint | For an n×n matrix, det(adj A) = (det A)n−1 | Using the power n instead of n−1 |
| System of linear equations | Unique solution, no solution or many solutions, decided by the determinant and further checks | Declaring many solutions when the determinant is zero, without checking the equations |
| Symmetric and skew-symmetric matrices | AT = A for symmetric, AT = −A for skew-symmetric; every square matrix splits into one of each kind | Forgetting that diagonal entries of a skew-symmetric matrix are zero |
| Powers of a matrix | Find A2 and A3, spot the pattern, then generalise | Arithmetic slips in the first multiplication |
| Matrix equations | Use the identity matrix, which leaves any matrix unchanged when multiplied | Cancelling a matrix as if it were a number |
Note that transpose (written AT) means swapping the rows and columns of a matrix. The adjoint of a matrix is the transpose of its cofactor matrix. Your child should be able to say both in one sentence.
A worked example: adjoint and determinant together
Question. A is a 3×3 matrix with det(A) = 2. Find det(adj A) and det(2A).
Step 1. For a 3×3 matrix, n = 3. So det(adj A) = (det A)n−1 = 22 = 4.
Step 2. Multiplying a 3×3 matrix by 2 multiplies each of its three rows by 2. Each row brings out a factor of 2. So det(2A) = 23 × det(A) = 8 × 2 = 16.
Why this matters. No long expansion was needed. The student only had to know two properties. Many questions in this chapter are built so that properties save time.
Ask your child to explain Step 2 aloud. A common mistake is to take the factor 2 out only one time. The factor comes out once for every row, so a 3×3 matrix gives 2 cubed.
How a tutor helps in this chapter
This chapter needs a person watching the working, not only the final answer. A tutor sitting next to the student can see exactly where a sign went wrong. A printed solution cannot do that.
- Finds the habit behind the error. If three mistakes come from the same weak habit, the tutor fixes the habit once.
- Teaches the choice of method. For each question, the tutor asks: should we expand, use row operations, or use a property? The student learns to choose before calculating.
- Keeps the pace right. Some students rush. Others re-check everything and run out of time. A tutor adjusts for each.
- Links school and JEE work. The tutor can use the school syllabus as the base and then raise the difficulty step by step.
Great Home Tutors offers one-to-one tuition at the student's home. It does not run a coaching centre or a group batch. The process is simple. You tell us the class, subject, board and locality. A person from our team calls you back to understand the student. A first class then lets you see the fit before anything is fixed. Tutors we have checked ourselves carry a Verified mark and are listed first. We also tell you plainly when a tutor is not verified yet.
A weekly practice plan
This plan suits a Class 12 student who also has school work. Change the days to fit your family's routine. The idea matters more than the exact days.
- Day 1, concept session with the tutor. Take one sub-topic only, such as adjoint and inverse. The student solves NCERT-level questions while the tutor watches the working.
- Day 2, same sub-topic, alone. The student solves a fresh set of the same type. Mark the questions that felt slow, not only the wrong ones.
- Day 3, properties revision. Write the main properties from memory on one page. Then check against the textbook and correct.
- Day 4, tutor session on mixed questions. The tutor mixes the types, so the student must first identify the type. This skill matters a great deal in JEE Main.
- Day 5, error notebook. Copy every mistaken question into a separate notebook. Write the cause in one line, such as a sign slip or a wrong formula.
- Day 6, timed set. Choose a fixed number of questions and a fixed time. Keep the same limits for a few weeks so progress is easy to see.
- Day 7, rest. A tired student makes careless errors. Rest is part of the plan.
Each week, rotate the sub-topic. Start with determinant properties, then adjoint and inverse, then linear equations, then matrix types and powers. In later weeks, run all the types together.
What parents can do without knowing the maths
- Check that the error notebook exists and is updated. You do not need to understand the content to see this.
- Ask your child to teach you one property each week. Explaining is a strong test of understanding.
- Protect study hours and sleep. Do not add extra practice sets when your child is already tired.
- Talk to the tutor about progress by question type, not only by marks. A note that adjoint questions are steady while linear equations need more work tells you far more than a single score.
Results depend on the student's effort and starting point. No routine can promise a rank or a result. A steady routine does make progress visible.
Key takeaways
- Learn the properties of determinants and adjoints. They shorten many JEE Main questions.
- Practise by question type first, then mix the types.
- Keep an error notebook and write the cause of each mistake in one line.
- Use NCERT as the base, then move to harder JEE-style questions.
- A tutor helps most by watching the working and correcting habits early.
Frequently asked questions
When should my child start this chapter for JEE Main?
Start when the school reaches it in Class 12, or earlier if your child has finished the basics in Class 11. Begin with NCERT questions so the base is firm. Add JEE-style practice once the basics feel steady.
How many tutor sessions a week does this plan need?
The plan above uses two tutor sessions and keeps the rest for self-practice. The student's own practice matters as much as the tutor's session. Talk to the tutor about what suits your child's schedule.
Can a tutor come to our home in Dwarka or Gurugram?
Great Home Tutors offers one-to-one tuition at your home. Tell us the class, subject, board and your locality, and a person from our team calls you back to understand the student.
How do I know whether the tutor has been checked?
Tutors we have checked ourselves carry a Verified mark and are listed first. We say clearly when a tutor is not verified yet, so you can decide with full information.
Does my child need to memorise every formula?
No. Understand why each property holds, and memorise only the short list in the table above. Revisit that list weekly until it comes without effort.
What to do next. Try it yourself on the page below.
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