In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 pdf, free NCERT solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 book pdf download.

Board | CBSE |

Textbook | NCERT |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 3 |

Chapter Name | Matrices |

Exercise | Ex 3.3 |

Number of Questions Solved | 12 |

Category | NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3

**Ex 3.3 Class 12 Maths Question 1.****Find the transpose of each of the following matrices:****(i)****(ii)****(iii)****Solution:**

(i) let A =

∴ transpose of A = A’ =

**Ex 3.3 Class 12 Maths Question 2.****If****then verify that:****(i) (A+B)’=A’+B’****(ii) (A-B)’=A’-B’****Solution:**

**Ex 3.3 Class 12 Maths Question 3.****If****then verify that:****(i) (A+B)’ = A’+B’****(ii) (A-B)’ = A’-B’****Solution:**

**Ex 3.3 Class 12 Maths Question 4.****If****then find (A+2B)’****Solution:**

**Ex 3.3 Class 12 Maths Question 5.****For the matrices A and B, verify that (AB)’ = B’A’, where****Solution:**

**Ex 3.3 Class 12 Maths Question 6.****If (i) ,the verify that A’A=I****If (ii) ,the verify that A’A=I****Solution:**

(i)

**Ex 3.3 Class 12 Maths Question 7.****(i) Show that the matrix is a symmetric matrix.****(ii) Show that the matrix is a skew-symmetric matrix.****Solution:**

(i) For a symmetric matrix a_{ij} = a_{ji}

Now,

**Ex 3.3 Class 12 Maths Question 8.****For the matrix,****(i) (A+A’) is a symmetric matrix.****(ii) (A-A’) is a skew-symmetric matrix.****Solution:**

=>

**Ex 3.3 Class 12 Maths Question 9.****Find and ,when****Solution:**

**Ex 3.3 Class 12 Maths Question 10.****Express the following matrices as the sum of a symmetric and a skew-symmetric matrix.****(i)****(ii)****(iii)****(iv)****Solution:**

(i) let

=>

**Ex 3.3 Class 12 Maths Question 11.****Choose the correct answer in the following questions:****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****Solution:**

Now A’ = B, B’ = B

(AB-BA)’ = (AB)’-(BA)’

= B’A’ – A’B’

= BA-AB

= – (AB – BA)

AB – BA is a skew-symmetric matrix Hence, option (a) is correct.

**Ex 3.3 Class 12 Maths Question 12.****If then A+A’ = I, if the****value of α is****(a)****(b)****(c) π****(d)****Solution:**

Now

Thus option (b) is correct.

**All Chapter NCERT Solutions For Class12 Maths**

—————————————————————————–**All Subject NCERT Solutions For Class12**

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