Chapter 3 : Matrices - Ncert Solutions for Class 12-science Maths CBSE

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.

Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.

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Chapter 3 - Matrices Exercise Ex. 3.1

Solution 1
Solution 2
Solution 3
Solution 4

Let A =

(i)

a11 = ,

a12 = ,

a21 = ,

a22 =

Therefore, A =

(ii)

a11 = ,

a12 = ,

a21 = ,

a22 =

Therefore, A =

(iii)

a11 = ,

a12 = ,

a21 = ,

a22 =

Therefore, A = . 

Solution 5

Solution 6

Solution 7
Solution 8
Solution 9

Solution 10

Chapter 3 - Matrices Exercise Ex. 3.2

Solution 1

Solution 2
Solution 3


(i) begin mathsize 12px style open square brackets table row straight a straight b row cell negative straight b end cell straight a end table close square brackets end stylebegin mathsize 12px style open square brackets table row straight a cell negative straight b end cell row straight b straight a end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell straight a squared plus straight b squared end cell cell negative ab plus ab end cell row cell negative ab plus ab end cell cell straight b squared plus straight a squared end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell straight a squared plus straight b squared end cell 0 row 0 cell straight a squared plus straight b squared end cell end table close square brackets end style

ii)begin mathsize 12px style open square brackets table row 1 row 2 row 3 end table close square brackets open square brackets table row 2 3 4 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 2 3 4 row 4 6 8 row 6 9 12 end table close square brackets end style

iii)begin mathsize 12px style open square brackets table row 1 cell negative 2 end cell row 2 3 end table close square brackets space open square brackets table row 1 2 3 row 2 3 1 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 1 minus 4 end cell cell 2 minus 6 end cell cell 3 minus 2 end cell row cell 2 plus 6 end cell cell 4 plus 9 end cell cell 6 plus 3 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell negative 3 end cell cell negative 4 end cell 1 row 8 13 9 end table close square brackets end style

iv)begin mathsize 12px style open square brackets table row 2 3 4 row 3 4 5 row 4 5 6 end table close square brackets space space open square brackets table row 1 cell negative 3 end cell 5 row 0 2 4 row 3 0 5 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 2 plus 0 plus 12 end cell cell negative 6 plus 6 plus 0 end cell cell 10 plus 12 plus 20 end cell row cell 3 plus 0 plus 15 end cell cell negative 9 plus 8 plus 0 end cell cell 15 plus 16 plus 25 end cell row cell 4 plus 0 plus 18 end cell cell negative 12 plus 10 plus 0 end cell cell 20 plus 20 plus 30 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 14 0 42 row 18 cell negative 1 end cell 56 row 22 cell negative 2 end cell 70 end table close square brackets end style

v)begin mathsize 12px style open square brackets table row 2 1 row 3 2 row cell negative 1 end cell 1 end table close square brackets open square brackets table row 1 0 1 row cell negative 1 end cell 2 1 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 2 minus 1 end cell cell 0 plus 2 end cell cell 2 plus 1 end cell row cell 3 minus 2 end cell cell 0 plus 4 end cell cell 3 plus 2 end cell row cell negative 1 minus 1 end cell cell negative 0 plus 2 end cell cell negative 1 plus 1 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 1 2 3 row 1 4 5 row cell negative 2 end cell 2 0 end table close square brackets end style

vi)begin mathsize 12px style open square brackets table row 3 cell negative 1 end cell 3 row cell negative 1 end cell 0 2 end table close square brackets open square brackets table row 2 cell negative 3 end cell row 1 0 row 3 1 end table close square brackets end style

begin mathsize 12px style equals open square brackets table row cell 6 minus 1 plus 9 end cell cell negative 9 plus 0 plus 3 end cell row cell negative 2 plus 0 plus 6 end cell cell 3 plus 0 plus 2 end cell end table close square brackets end style

begin mathsize 12px style equals open square brackets table row 14 cell negative 6 end cell row 4 5 end table close square brackets end style

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Solution 8
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Solution 11
Solution 12
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Solution 15

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Solution 17
Solution 18

Solution 19

Solution 20
Solution 21
Solution 22

Chapter 3 - Matrices Exercise Ex. 3.3

Solution 1
Solution 2

Solution 3

Solution 4
Solution 5

Solution 6

Solution 7

Solution 8
Solution 9
Solution 10

Solution 11



Solution 12
Solution 13

Chapter 3 - Matrices Exercise Ex. 3.4

Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6

Solution 7

Solution 8
Solution 9
Solution 10

Let A =

Now, det(A)=|A|=6-4=2≠0

Therefore, inverse of A exist.

We know that, A=AI

 ….. (C2→C2+ C1)

 ….. (C1→C1+6C2)

 ….. (C1→ C1)

 ….. (C2→ C2)

 

Solution 11

Solution 12
Solution 13
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Solution 17

Solution 18

Chapter 3 - Matrices Exercise Misc. Ex.

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Solution 2

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Solution 10

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Solution 11


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Why CBSE Class 12 Science Maths solutions are important?

Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking the logical way to solve maths problems. For practising problems, study materials such as sample papers, previous year papers, and NCERT solutions are needed.

Some of the best Maths experts work with us to give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for Class 12 Science Maths can be easily accessible on TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions, and more.

To prepare for your Maths exam, you need to attempt solving different kinds of Maths questions. One of the best ways to assess your problem-solving abilities is to attempt solving previous year papers with a set timer. Our Maths solutions will come in handy to help you with checking your answers and thus, improving your learning experience. So, to score more marks in your Class 12 board exams, use our Maths solutions that will enable you with the appropriate preparation.