1. Home
  2. |  
  3. CBSE Board|  

NCERT Solutions for CBSE Class 12 Mathematics ‒ Chapter 3: Matrices (Part II)

Jul 7, 2017 16:00 IST

    NCERT Solutions for CBSE Class 12 Mathematics ‒ Chapter 3: Matrices (Part II)

    NCERT Solutions for CBSE 12th Maths, Chapter 3: Matrices are available here. In this article, you will find solutions of exercise 3.1 (from question number 6 to question number 10). These questions are mainly based on equality of Matrices. These questions are also important for CBSE Class 12 board exam 2018 and other engineering entrance exams.

    Question 6:


    Solution 6:

    (i)

    In the given matrix, if we compare the corresponding elements, x = 1, y = 4, and z = 3.

    (ii)

    In the given matrix, on comparing the corresponding elements, we have,

    x + y = 6

    xy = 8

    ⇒ 5 + z = 5 ⇒ z = 0

    Now, (xy)2 = (x + y)2 − 4xy

    ⇒ (xy)2 = 36 − 32 = 4

    xy = ±2

    ∴x = 4, y = 2, and z = 0 or x = 2, y = 4, and z = 0.

    (iii)

    Comparing the corresponding elements,

    x + y + z = 9 … (1)

    x + z = 5 …..... (2)

    y + z = 7 …..... (3)

    From …(1) and ….(2)

    y + 5 = 9 ⇒ y = 4

    Then, from (3) 4 + z = 7

    z = 3 ∴ x + z = 5

    x = 2

    ∴ x = 2, y = 4, and z = 3

    NCERT Exemplar Class 12 Mathematics – Chapter 3: Matrics

    Question 7:


    Solution 7:

    Comparing the corresponding elements,

    ab = −1 … (1)

    2ab = 0 … (2)

    2a + c = 5 … (3)

    3c + d = 13 … (4)

    From equation …(2)

    b = 2a

    From (1), a − 2a = −1

    ⇒ a = 1 ⇒ b = 2

    From (3), 2 ×1 + c = 5

    c = 3

    From equation (4), 3 ×3 + d = 13

    ⇒ 9 + d = 13

    d = 4

    ∴ a = 1, b = 2, c = 3, and d = 4.

    Question 8: A = [aij]m × n is a square matrix, if

    (A) m < n

    (B) m > n

    (C) m = n

    (D) None of these

    Solution 8:

    We know that, A given matrix is said to be a square matrix if the number of rows is equal to the number of columns. The correct answer is C.

    A = [aij]m × n is a square if m = n.

    Question 9:


    Solution 9:

    On comparing the corresponding elements, we have,

    3 x + 7 = 0

    x = ‒7/3

    Also, 5 = y ‒ 2 ⇒ y = 7

    Again, y + 1 = 8

    y = 7.

    Also,

    2 ‒ 3x = 4

    x = ‒2/3.

    Question 10: The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:

    (A) 27

    (B) 18

    (C) 81

    (D) 512

    Solution 10:

    Elements of a 3 × 3 matrix = 9.

    Each of these elements can be either 0 or 1.

    Each of the 9 elements can be filled in two possible ways.

    Therefore, by the multiplication principle, the required number of possible matrices is 29 = 512.

    Download NCERT Solutions for Class 12 Maths (Chapter 3 - Matrices) in PDF format

    DISCLAIMER: JPL and its affiliates shall have no liability for any views, thoughts and comments expressed on this article.

    Latest Videos

    Register to get FREE updates

      All Fields Mandatory
    • (Ex:9123456789)
    • Please Select Your Interest
    • Please specify

    • ajax-loader
    • A verifcation code has been sent to
      your mobile number

      Please enter the verification code below

    This website uses cookie or similar technologies, to enhance your browsing experience and provide personalised recommendations. By continuing to use our website, you agree to our Privacy Policy and Cookie Policy. OK
    X

    Register to view Complete PDF