Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 12 Mathematics I 3. Matrices to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 12 Mathematics I 3. Matrices to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 3.2. Whether you are studying for board exams or mid-term exams, 12 Mathematics I Chapter 3. Matrices solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise 3.2
Ques.1. Let A = 
B = 
C = 
. Find each of the following:
(i) A + B
(ii) A – B
(iii) 3A – C
(iv) AB
(v) BA
Ans. (i) A + B = 
= 
(ii) A – B = 
= 
(iii) 3A – C = 
= 
(iv) AB = 
= 
(v) BA = 
= 
Ques.2. Compute the following:
(i) 
(ii) 
(iii) 
(iv) 
Ans. (i) = 
(ii)
= 
(iii) = 
(iv) = 
Ques.3. Compute the indicated products:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Ans. (i) = 
(ii) = 
(iii) = 
(iv)
= 
= 
(v)
= 
(vi)
= 
Ques.4. If A = 
B = 
and C = 
then compute (A + B) and (B – C). Also, verify that A + (B – C) = (A + B) – C.
Ans. A + B = 
= 
= 
B – C = 
= 
= 
Now, A + (B – C) = (A + B) – C
= 
= 
=
L.H.S. = R.H.S.
hance Proved.
and B = 
then compute 3A – 5B.Ans. 3A – 5B = 
= 
= 
Ques.6. Simplify: 
Ans. Given:
= 
= 
(i) X + Y = 
and X – Y = 
(ii) 2X + 3Y = 
and 3X + 2Y = 
Ans. (i) Given: X + Y = …..(i)
and X – Y = …..(ii)
Adding eq. (i) and (ii), we get
2X = 
X = 
Subtracting eq. (i) and (ii), we get
2Y = 
Y = 
(ii) Given: 2X + 3Y = …..(i)
and 3X + 2Y = 
…..(ii)
Multiplying eq. (i) by 2, 4X + 6Y = 
……….(iii)
Multiplying eq. (ii) by 3, 9X + 6Y = 
………(iv)
subtracting Eq. (iii) from Eq. (iv)
5X = 
= 
X = 
Now, From eq. (i), 3Y = 
2X = 
3Y = 
= 
Y = 
and 2X + Y = 
Ans. 2X + Y = 
2X = – Y
2X = 
2X = 
X = 
= 
and 
if 
Ans. Given: 
Equating corresponding entries, we have
and 
and 
and 
and 
and 
if 
Ans. Given: 
Equating corresponding entries, we have
And 
And 
And 
, , ,
find the values of and 
Ans. Given: 
Equating corresponding entries, we have
……….(i) and 
……….(ii)
Adding eq. (i) and (ii), we have 
Putting in eq. (ii), 
find the values of and 
Ans. Given: 
Equating corresponding entries, we have
And 
And 
……….(i)
And 
Putting in eq. (i), 
, , ,
show that 
Ans. Given: 
……….(i)
Changing to 
in eq. (i), 
L.H.S. = 
= 
= 
= 
= R.H.S. [changing to 
in eq. (i)]
(i) 
(ii) 
Ans. (i) L.H.S. = 
= 
= 
R.H.S. = 
= 
= 
L.H.S. 
R.H.S.
(ii) L.H.S. = 
= 
= 
R.H.S. = 
= 
= 
L.H.S. R.H.S.
.Ans. A2 – 5A + 6I = 
= 
= 
= 
= 
prove that A3 – 6A2 + 7A + 2I = 0.Ans. L.H.S. = A3 – 6A2 + 7A + 2I
= 
= 
= 
= 
= 
= 
= 
= 
= 0 (Zero matrix)
= R.H.S.
hance Proved.
and I = 
find 
so that 
Ans. Given: A = and I =
Equating corresponding entries, we have
And 
and 
and I is the identity matrix of order 2, show that
Ans. L.H.S. = I + A = 
and, I – A = 
R.H.S. = 
= 
= 
= 
= 
= 
= 
= 
L.H.S. = R.H.S.
hance Proved.
Ans. Let the investment in first bond = ,
investment in the second bond = `
Interest paid by first bond = 5% = 
per rupee and
interest paid by second bond = 5% = 
per rupee.
Matrix of investment is A = 
Exercise 3.2 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 12 Mathematics I Chapter 3. Matrices solutions help you understand the core concepts and practice effectively.
Revision is the key to exam success. Our notes for 12 Mathematics I highlight important formulas, key definitions, and exam-ready points from Chapter 3. Matrices. These quick revision notes make last-minute preparation easy.
Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 3.2 include complete solutions for 12 Mathematics I Chapter 3. Matrices exercises. With step-by-step answers, you gain clarity and confidence to attempt similar exam questions.
To boost your preparation, we also provide additional important questions with answers. These are prepared from previous year board papers, sample papers, and important concepts of Chapter 3. Matrices. Practicing these ensures you are well-prepared for both board and mid-term exams.
Our Exercise 3.2 are useful for both board exams and mid-term exams. For 12 Mathematics I, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 3.2 for 12 Mathematics I Chapter 3. Matrices are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
Go to other Class
Download worksheets and assignments for better practice and revision.