• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2020
    • RBSE Class 10th Board Model Papers 2020
    • RBSE Class 8th Board Model Papers 2020
    • RBSE Class 5th Board Model Papers 2020
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

May 24, 2019 by Fazal Leave a Comment

Rajasthan Board RBSE Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 1.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find A.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 2.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find (A – 2I) (A – 3I).
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 3.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find AB.
Solution:

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 4.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find BA.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 5.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find matrices A and B.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 6.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find the value of x and y.
Solution:
On comparing,
x + 2 = -2 ∴ x = -4
– y – 2 = 5 ⇒ y = -7

Hence, x = -4, y = -7

Question 7.
Order of matrix A is 3 x 4 and B is a matrix, such that ATB and ABT defined, then write the order of B.
Solution:
∴ Order of A = 3 x 4
∴ Order of AT = 4 x 3
But ATB and ABT is defined.
So, order of B is 3 x 4.

Question 8.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , is a symmetric matrix, then determine x.
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
On comparing aij = aji
a32 = a23 ⇒ -x = 4
∴ x = -4

Question 9.
Construct a matrix of order 3 x 3, B = [bij], whose elements are bij= (i) (j).
Solution:
B11 = 1 x 1 = 1
B12 = 1 x 2 = 2
B13 = 1 x 3 = 3

B21 = 2 x 1 = 2
B22 = 2 x 2 = 4
B23 = 2 x 3 = 6

B31 = 3 x 1 = 3
B32 = 3 x 2 = 6
B33 = 3 x 3 = 9
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 10.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Solution:

Question 11.
Express matrix A as the sum of symmetric and skew-symmetric matrices, where
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise .
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 12.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise then prove that :
(i) (AT)T = A
(ii) A + AT is a symmetric matrix.
(iii) A – AT is a skew-symmetric matrix.
(iv) AAT and ATA are symmetric matrix.
Solution:
(i) (AT)T = A
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

(ii) A + AT is symmetric
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
So, A + AT is symmetric matrix. Hence Proved.

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
So, A – AT is skew symmetric matrix. Proved.

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Here,
a21 = a12 = 0
a31 = a13 = 0
a23 = a32 = 6
So, AAT is symmetric matrix.

RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Here,
a12 = a21 = 0
a13 = a31 = 0
a32 = a23 = 4
So, ATA is symmetric matrix.

Question 13.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , and 3A – 2B + C is a null matrix, then determine matrix ‘C’.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 14.
Construct a matrix B = [bij] of the order 2 x 3, whose elements are bij = (i +2j)2/2
Solution:
Given, B = [bij] whose elements are
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 15.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find the element of 1st row of ABC.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
So, element of 1st row is 8.

Question 16.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise, then find AAT.
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 17.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find x.
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 18.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise, then prove
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
= (bc – ad)I2 = R.H.S.
Hence Proved.

Question 19.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find the matrix form of the following (aA + bB) (aA – bB).
Solution:
Givn,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 20.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then prove that (A – B)2 ≠ A2 – 2AB + B2.
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
From (i) and (ii),
(A – B)2 + A2 – 2AB + B2
Hence Proved.

Question 21.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise , then find k, where A2 = kA – 2IA2 .
Solution:
Given,
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
On comparing corresponding element
From 3k – 2 = 1
3k = 3 ⇒ k = \frac { 3 }{ 3 } ⇒ k = 1.

Question 22.
i = √-1 then prove that :
(1) A2 = B2 = C2 = -I2
(ii) AB = – BA = -C
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 23.
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise and f(A) = A2 – 5A + 7I then find f(A).
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

Question 24.
Prove that
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

RBSE Solutions for Class 12 Maths

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)
  • Click to share on Google+ (Opens in new window)

Related

Filed Under: Class 12

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Recent Posts

  • RBSE Solutions for Class 11 Maths Chapter 2 Relations and Functions Ex 2.4
  • Rajasthan Board Class 12 Books | RBSE 12th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 11 Books | RBSE 11th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 10 Books | RBSE 10th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 9 Books | RBSE 9th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 8 Books | RBSE 8th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 7 Books | RBSE 7th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 6 Books | RBSE 6th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 5 Books | RBSE 5th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 4 Books | RBSE 4th Class Books PDF Download in English Hindi Medium
  • Rajasthan Board Class 3 Books | RBSE 3rd Class Books PDF Download in English Hindi Medium

Footer

Copyright © 2021 · Magazine Pro on Genesis Framework · WordPress · Log in