# 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

**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** 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

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}Maths* CBSE Class 12^{th}* 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

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}MathsAs 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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