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# NCERT Solutions for Class 12 Maths Matrices

Hi Students, Welcome to Amans Maths Blogs (AMB). In this post, you will get the NCERT Solutions for Class 12 Maths Matrices Exercise 3.3. This NCERT Solutions can be downloaded in PDF file. The downloading link is given at last.

NCERT Solutions for Class 12 Maths are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of CBSE Class 12th Maths like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.

CBSE Class 12th is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So CBSE NCERT Solutions for Class 12th Maths is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.

As we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the CBSE NCERT Syllabus. Thus, NCERT Solutions helps the students to solve the exercise questions as given in NCERT Books.

## NCERT Solutions for Class 12 Maths Matrices Exercise 3.3

NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 1.

Find the transpose of each of the following matrices:

(i)

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(ii)

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(iii)

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 2.

If , then show that

(i) (A + B)′ = A′ + B′,

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(ii) (A – B)′ = A′ – B′,

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 3.

If , then show that

(i) (A + B)′ = A′ + B′,

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(ii) (A – B)′ = A′ – B′,

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 4.

If , then find (A + 2B)′

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 5.

For the matrices A and B, verify that (AB)′ = B′A′, where

(i)

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(ii)

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 6.

For the matrices A and B, verify that (AB)′ = B′A′, where

(i) If , then verify that A′ A = I.

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(ii) If , then verify that A′A = I.

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 7.

(i) Show that the matrix  is a symmetric matrix.

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(ii) Show that the matrix is a symmetric matrix.

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 8.

For the matrix , verify that

(i)(A + A′) is a symmetric matrix.

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(ii)(A – A′) is a skew symmetric matrix

NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 9.

Find

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 10.

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i)

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(ii)

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(iii)

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(iv)

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NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 11.

If A, B are symmetric matrices of same order, then AB – BA is a

(A) Skew symmetric matrix

(B) Symmetric matrix

(C) Zero matrix

(D) Identity matrix

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We know that A’ = A and B’ = B.

Thus. (AB – BA)’ = B’A’ – A’B’ = BA – AB = -(AB – BA).

Therefore, (AB – BA) is a skew symmetric.

NCERT Solutions for Class 12 Maths Matrices Exercise 3.3: Ques No 12.

If , then A + A′ = I, if the value of α is

(A) π/6

(B) π/3

(C) π

(D) 3π/2

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