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Chapter 3 – Matrices Exercise 3.1
1.
Ans – (i) Order of the given matrix A is 3 x 4
(ii) Number of elements will be 3 * 4 = 12
(iii) a13 = 19, a21 = 35, a33 = -5, a24 = 12, a23 = 5/2
2.
Ans – In order to get the possible orders of matrix with 24 elements we need to find all the pair of natural numbers whose product will be 24. They are (1 × 24), (24 × 1), (2 × 12), (12 × 2), (3 × 8), (8 × 3), (4 × 6), (6 × 4).
Similarly for 13 elements is will be (13 x 1) and (1 x 13).
3.
Ans – In order to get the possible orders of matrix with 18 elements we need to find all the pair of natural numbers whose product will be 18. They are (1 × 18), (18 × 1), (2 × 9), (9 × 2), (3 × 6), (6 × 3).
Similarly for 5 elements is will be (5 x 1) and (1 x 5).
4.
Flashcard for Question 4
Common Mistake:
Confusing i and j order — remember i is row, j is column.
Exam Insight:
This is a direct substitution problem – speed comes from calculating entries in a fixed order: (1,1), (1,2), (2,1), (2,2).
5.
Flashcard for Question 5
Short Formula Recall:
For a matrix [a_ij], i is row number (1 to 3) and j is column number (1 to 4). Substitute values directly into the given formula for each element.
Quick Tip:
Always handle the modulus (absolute value) first before dividing or simplifying.
Common Mistake:
Forgetting that |x| makes negative values positive, which can flip signs unexpectedly.
Exam Insight:
Matrix construction problems test indexing accuracy – consistent calculation order reduces silly errors.
6.
Flashcard for Question 6
Short Formula Recall:
Equality of matrices ⇒ corresponding entries are equal: a_ij = b_ij for all i, j.
Quick Tip:
Match (1,1), (1,2), (2,1), (2,2) positions on both sides and read off x, y, z directly.
Common Mistake:
Mixing up row/column indices or trying to solve extra equations instead of simple term-by-term matching.
7.
Flashcard for Question 7
Quick Tip:
Write four separate equations from element-by-element matching, then solve systematically (often a and b come first from the first two equations in a column).
Common Mistake:
Overcomplicating with determinants or inverses—this is just direct comparison, no matrix operations needed.
8.
9.
10.
Ans – Given 3 x 3 matrix means it will have 9 elements. Each element can be filled in two possible ways i.e. 0 or 1. So the number of all possible matrices will be 29 = 512. Hence option D is the correct answer.
Download Exercise 3.1 NCERT Solutions PDF
You can download the PDF from the link below for offline study
Class 12 Maths Chapter 3 – Matrices: All Exercises
| Exercise | Link |
|---|---|
| Exercise 3.2 | View Solutions |
| Exercise 3.3 | View Solutions |
| Exercise 3.4 | View Solutions |
Class 12 Matrices- Exercise 3.1 Overview
Learning about matrices is like learning a new math language. That voyage starts with Exercise 3.1. The chapter on matrices in the 2025 NCERT syllabus for Class 12 Maths has been completely rewritten to make sure that the essential notions are stronger. This project helps students learn what matrices are and what kinds there are, like row, column, square, diagonal, and more. Students will learn how to sort and recognize different matrices by reading this part of the chapter. This is a very crucial step in learning how to use math data in a productive way.
Matrices Class 12 NCERT Solutions Exercise 3.1 is really helpful since it helps you make clear ideas. It teaches pupils how to build, write, and arrange matrices before they have to do complex math. This helps kids get better at math and their visual reasoning. These approaches make it easier and less stressful to study, whether you’re a student getting ready for board examinations or just want to get better at arithmetic.
The new syllabus for 2025 puts a lot of emphasis on how things work in the real world, and matrices are no different. You can use matrices for more than simply math. They are utilized in data science, statistics, computer graphics, and engineering problems. Matrices Class 12 NCERT Solutions Exercise 3.1 is a good place to start if you want to understand how to employ theoretical notions in real life and when solving difficulties.
There are more than simply problems in this exercise; it’s an opportunity to see Math in a new manner. Matrices Class 12 NCERT Solutions Exercise 3.1 helps students understand the basics by giving them step-by-step explanations, real-world examples, and unambiguous answers that focus on the test. This way, everyone feels safe as they learn. This material will help you keep ahead, whether you’re learning something new or going over what you’ve already studied.
FAQs –Matrices Class 12 Exercise 3.1 NCERT
A lot of students have trouble with Exercise 3.1 since they have never heard of matrices before. Without good examples and a clear picture, words like “order of a matrix” and “types of matrices” might be hard to understand.
Making a tiny chart or flashcards with 1–2 examples for each form of matrix—row, column, square, diagonal, and zero matrix—is an excellent idea. Visual association helps you remember things better.
You should know exactly what a matrix is, what the notation means, and how to find the order. At this point, it’s also very important to be able to recognize matrix types apart from their elements.
The order of a matrix is usually represented as rows times columns. Writing out the orders of a few matrices by hand can help you remember this format.
It’s better to look for patterns in the elements of a matrix than to look for shortcuts. If there is only one row, it is a row matrix. If all of the non-diagonal components are zero, it is a diagonal matrix.
The Matrices Class 12 NCERT Solutions Exercise 3.1 gives you a step-by-step way to classify and reason, so you not only get the right answer but also know why it’s the right type.
Very important. Exercise 3.1 is the basis for the next exercises, which will include matrix operations, transposition, and inverses. If you don’t understand this well, it will be more harder to learn about other things later.