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NCERT Solutions For Class 12 Maths Chapter 3 Matrices Ex 3.1

Here, Below you all know about NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1 Question Answer. I know many of you confuse about finding Chapter 3 Matrices Ex 3.1 Of Class 12 NCERT Solutions. So, Read the full post below and get your solutions.

TextbookNCERT
BoardCBSE
CategoryNCERT Solutions
ClassClass 12
SubjectMaths
ChapterChapter 3
ExerciseClass 12 Maths Chapter 3 Matrices Exercise 3.1
Number of Questions Solved10
NCERT Solutions For Class 12 Maths Chapter 3 Matrices Ex 3.1

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1

NCERT TEXTBOOK EXERCISES

Ex 3.1 Class 12 Maths Question 1.
In the matrix $A=\left[ \begin{matrix} 2 \ 35 \ \sqrt { 3 } \end{matrix}\begin{matrix} 5 \ -2 \ 1 \end{matrix}\begin{matrix} 19 \ 5/2 \ -5 \end{matrix}\begin{matrix} -7 \ 12 \ 17 \end{matrix} \right]$
(i) The order of the matrix
(ii) The number of elements
(iii) Write the elements a13, a21, a33, a24, a23

Solution:

(i) The matrix A has three rows and 4 columns.
The order of the matrix is 3 x 4.
(ii) There are 3 x 4 = 12 elements in the matrix A
(iii) a13 = 19, a21 = 35, a33 = – 5, a24 = 12, a23 = 5/2

Ex 3.1 Class 12 Maths Question 2.
If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Solution:

(i) 24 = 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6
Thus there are 8 matrices having 24 elements their order are (1 x 24), (24 x 1), (2 x 12), (12 x 2),(3 x 8), (8 x 3), (4 x 6), (6 x 4).
(ii) 13 = 1 x 13,
There are 2 matrices of 13 elements of order (1 x 13) and (13 x 1).

Ex 3.1 Class 12 Maths Question 3.
If a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements.

Solution:

We know that if a matrix is of order m × n, it has mn elements.
=> 18 = 1 x 18 = 2 x 9 = 3 x 6
Thus, all possible ordered pairs of the matrix
having 18 elements are:
(1,18), (18,1), (2,9), (9,2), (3,6), (6,3)
If it has 5 elements, then possible order are: (1,5), (5,1)

Ex 3.1 Class 12 Maths Question 4.
Construct a 2 x 2 matrix, A= [aij] whose elements are given by:

$(i)\quad { a }_{ ij }=\frac { { (i+j) }^{ 2 } }{ 2 }$
(ii)aij=i/j
$(iii)\quad { a }_{ ij }=\frac { { (i+2j) }^{ 2 } }{ 2 }$

Solution:

$A={ \left[ { a }{ ij } \right] }{ 2\times 2 }=\begin{bmatrix} { a }{ 11 } & { a }{ 12 } \ { a }{ 21 } & { a }{ 22 } \end{bmatrix}$
$(i)\quad { a }_{ ij }=\frac { { (i+j) }^{ 2 } }{ 2 }$

Ex 3.1 Class 12 Maths Question 5.
Construct a 3 x 4 matrix , whose elements are given by:
(i) $(i){ a }_{ ij }=\frac { 1 }{ 2 } \left| -3i+j \right|$
(ii)aij=2i−j

Solution:

$A={ \left[ { a }{ ij } \right] }{ 3\times 4 }=\left[ \begin{matrix} { a }{ 11 } \ { a }{ 21 } \ { a }{ 31 } \end{matrix}\begin{matrix} { a }{ 12 } \ { a }{ 22 } \ { a }{ 32 } \end{matrix}\begin{matrix} { a }{ 13 } \ { a }{ 23 } \ { a }{ 33 } \end{matrix}\begin{matrix} { a }{ 14 } \ { a }{ 24 } \ { a }{ 34 } \end{matrix} \right]$
$(i){ a }_{ ij }=\frac { 1 }{ 2 } \left| -3i+j \right|$

Ex 3.1 Class 12 Maths Question 6.
Find the values of x, y, z from the following equations:

$(i)\begin{bmatrix} 4 & 3 \ x & 5 \end{bmatrix}=\begin{bmatrix} y & z \ 1 & 5 \end{bmatrix}$
$(ii)\begin{bmatrix} x+y & 2 \ 5+z & xy \end{bmatrix}=\begin{bmatrix} 6 & 2 \ 5 & 8 \end{bmatrix}$
$(iii)\left[ \begin{matrix} \begin{matrix} x+ & y+ & z \end{matrix} \ \begin{matrix} x & +y \end{matrix} \ \begin{matrix} y & +z \end{matrix} \end{matrix} \right] =\left[ \begin{matrix} 9 \ 5 \ 7 \end{matrix} \right]$

Solution:

$(i)\begin{bmatrix} 4 & 3 \ x & 5 \end{bmatrix}=\begin{bmatrix} y & z \ 1 & 5 \end{bmatrix}$
Clearly x = 1,y = 4,z = 3
$(ii)\begin{bmatrix} x+y & 2 \ 5+z & xy \end{bmatrix}=\begin{bmatrix} 6 & 2 \ 5 & 8 \end{bmatrix}$
Now 5 + z = 5 => z = 0
Now x + y = 6 and xy = 8
∴ y = 6 – x and x(6 – x) = 8
6x – x² = 8
x² – 6x + 8 = 0
(x – 4)(x – 2) = 0
=>x = 2,4
When x = 2, y = 6 – 2 = 4
and when x = 4,y = 6 – 4 = 2
Hence x = 2,y = 4,z = 0 or x = 4,y = 2,z = 0.
(iii) Equating the corresponding elements.
=> x+y+z=9 …..(i)
x+z = 5 …(ii)
y+ z = 7 …(iii)
Adding eqs. (ii) & (iii)
x + y + 2z = 12
=> (x+y+z) + z = 12,
9+z = 12 (from equ (i))
z = 3
x + z = 5
=>x + 3 = 5 => x = 2
and y+z = 7
=>y+3 = 7
=> y = 4
=> x = 2, y = 4 and z = 3

Ex 3.1 Class 12 Maths Question 7.
Find the values of a,b,c and d from the equation:
$\begin{bmatrix} a-b & 2a+c \ 2a-b & 3c+d \end{bmatrix}=\begin{bmatrix} -1 & 5 \ 0 & 13 \end{bmatrix}$

Solution:

$\begin{bmatrix} a-b & 2a+c \ 2a-b & 3c+d \end{bmatrix}=\begin{bmatrix} -1 & 5 \ 0 & 13 \end{bmatrix}$

Ex 3.1 Class 12 Maths Question 8.
A = [aij]m×n is a square matrix, if
(a) m < n (b) n > n
(c) m = n
(d) none of these

Solution:

For a square matrix m=n.
Thus option (c) m = n, is correct.

Ex 3.1 Class 12 Maths Question 9.
Which of the given values of x and y make the following pairs of matrices equal:
$\begin{bmatrix} 3x+7 & 5 \ y+1 & 2-3x \end{bmatrix},\begin{bmatrix} 0 & y-2 \ 8 & 4 \end{bmatrix}$

(a) x=−1/3,y=7
(b) Not possible to find
(c) y=7,x=−2/3
(d) x=−1/3,y=−2/3

Solution:

$\begin{bmatrix} 3x+7 & 5 \ y+1 & 2-3x \end{bmatrix},\begin{bmatrix} 0 & y-2 \ 8 & 4 \end{bmatrix}$
(a) x=−1/3, y=7

Ex 3.1 Class 12 Maths 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:

There are 3 x 3 matrix or 9 entries in matrix each place can be filled with 0 or 1
∴ 9 Places can be filled in 29 = 512 ways
Number of such matrices = 512
Option (d) is correct.

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1 PDF

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