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NCERT Solutions for Class 12 Maths Chapter 3 – Matrices Exercise 3.2
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Chapter 3 – Matrices Exercise 3.2
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Flashcard for Question 2
Short Formula Recall: (A + B){ij} = A{ij} + B_{ij}. Also use identities: cos2x + sin2x = 1 and (a2+b2)/(a2+c2) stays elementwise (no cancellation unless same denominator).
Quick Tip: First check dimensions match; then add entry-by-entry left to right, top to bottom. For trig entries simplify using cos2x + sin2x = 1 immediately.
Common Mistake: Trying to add matrices of different sizes, swapping positions (adding wrong entries), or treating addition like multiplication. Also forgetting to apply trig identities (missing the 1) or sign errors with negatives.
Exam Insight: Show the dimension check, perform elementwise addition clearly (write results in matrix form), and simplify obvious identities cos2x + sin2x = 1) to save time and avoid lost marks.
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Flashcard for Question 4
Quick Tip: Perform matrix addition and subtraction entry-by-entry. Always align the corresponding positions before calculating.
Common Mistake: Mixing up subtraction order (B – C ≠ C – B), or adding/subtracting wrong elements across rows/columns.
Exam Insight: This problem checks associativity and compatibility of matrix addition/subtraction. Clearly show each intermediate step for (A + B) and (B – C), then verify that both sides of A + (B – C) = (A + B) – C match.
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Flashcard for Question 7
Quick Tip: Use simultaneous equations of matrices. For (i), add and subtract the two given equations to isolate X and Y. For (ii), treat 2X+3Y and 3X+2Y as a system, solve like linear equations but entry-wise.
Common Mistake: Forgetting to divide by 2 after adding/subtracting equations, or mixing elementwise operations with scalar multiplication.
Exam Insight: These problems test your ability to manipulate matrix equations exactly like algebraic ones. Show the step where you add/subtract equations clearly, then divide to get X and Y.
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Comparing corresponding elements we get,
3x = x + 4, ⇒ x = 2
3y = 6 + x + y, ⇒ y = 4
3z = -1 + x + w, ⇒ z = 1
3w = 2w + 3, ⇒ w = 3
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Flashcard for Question 15
Quick Tip: First compute A² = A x A. Then multiply A by 5, and add 6I(identity matrix with diagonal entries 6). Finally combine them as A² – 5A + 6I.
Common Mistake: Forgetting that I is the identity matrix (not a scalar), or doing elementwise squaring instead of proper matrix multiplication for A².
Exam Insight: This type of question checks accuracy in matrix multiplication and handling expressions with identity matrices. Write each step clearly: A², then -5A, then +6I, and finally combine them. This avoids small arithmetic slips that cost marks.
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Flashcard for Question 17
Quick Tip: Calculate A² before equating to equation to find k.
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Flashcard for Question 19
Quick Tip: Represent the problem as a system of linear equations using matrices:
x + y = 30000
0.05x + 0.07y = required interest (1800 or 2000).
Then solve using matrix inversion or elimination.
Common Mistake: Mixing up coefficients (e.g. writing 5 instead of 0.05), or forgetting to convert % into decimals, which gives wrong answers.
Exam Insight: Matrix form Ax = B is what the question tests. Clearly writing the system as a matrix equation and showing one correct method (like inverse or elimination) usually earns full marks, even if arithmetic is left simplified.
Ans – (a) Let’s assume Rs x is invested in first bond. Then the amount of money invested in second bond will be Rs (30000 – x). The first bond pays 5% interest per year, while the second bond pays 7% per year.
Thus, to obtain an annual total interest of Rs 1,800, we have:
(b) To obtain an annual total interest of Rs 2,000, we have:
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Ans – The bookshop sells ten dozen chemistry books, eight dozen physics books, and ten dozen economics books. The selling prices for chemistry, physics, and economics books are Rs 80, Rs 60, and Rs 40, respectively. The entire amount of money obtained from the sale of all these books can be represented in the form of a matrix as follows:
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Ans – Option A is the correct answer.
PY + WY = P(order of matrix, p x k) x Y(order of matrix, 3 x k) + W(order of matrix, n x k)
Y(order of matrix, 3 x k). So we get k = 3 and p = n.
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Ans – Option B is the correct answer.
We know n = p. ⇒ Order of matrices X and Z are same.
Order of 7X – 5Z is same as order of X and Z.
So we get order of 7X – 5Z is either 2 x n or 2 x p.
Download Exercise 3.2 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 3.1 | View Solutions |
| Exercise 3.3 | View Solutions |
| Exercise 3.4 | View Solutions |
Class 12 Matrices – Exercise 3.2 Overview
Answers to Class 12 NCERT Matrices Exercise 3.2 makes learning about matrices more entertaining by showing students how to add, subtract, and multiply matrices by a number. You learned how to execute operations between matrices in Exercise 3.1, and this exercise builds on that. The most important thing to understand is when operations are allowed, which is when the matrices are the same size.
This part of the textbook makes students more confident about how to handle matrix elements in a methodical way. Students learn how to add and subtract matrices by performing it one element at a time as they start Exercise 3.2. You also learn how to do scalar multiplication in this lesson. This is when you multiply each number in a matrix by a number. This prepares you to study about linear transformations in higher-level math and science.
Matrices Class 12 NCERT Solutions Exercise 3.2 is helpful since it shows you how to solve problems step by step. These answers help students recall the principles they need to follow when completing operations and stop them from making mistakes like mixing up the orders of matrices. Finding the answers is not enough; you also need to understand why each step works.
Students who are preparing ready for board exams should do this exercise over and over until they are very adept at basic matrix operations. Going over NCERT solutions in depth will help you get faster and more accurate because similar problems often crop up on tests. Students become ready to solve harder problems in the upcoming exercises by solving the problems from Matrices Class 12 NCERT Solutions Exercise 3.2 over and over again.
FAQs – Matrices Class 12 Exercise 3.2 NCERT
This happens a lot when students try to do things with matrices that are not in the same order. Always make sure that both matrices have the same number of rows and columns.
Think of scalar multiplication as giving each part of a matrix a number. To get used to it, try a few examples with positive, negative, and zero scalars.
It is not possible to add or subtract matrices of differing orders. To avoid making mistakes on board exams, it’s important to know this restriction.
This exercise lays the groundwork for more complicated matrix operations, such as multiplication and determining inverses. If you don’t know how to add and do scalar operations, those subjects will seem too hard.
They show the right processes and structure for each response, which makes it easy to do the same thing on tests and not lose points for not showing your work or formatting it wrong.