NCERT Solutions Class 12 Mathematics Chapter 3 Matrices Download In Pdf

Chapter 3 Matrices Download in pdf

**Question 1.** In the matrix
2 5 19 7
A 35 2 5 12
2
3 1 5 17 −
= −
, write:

(i) The order of the matrix,

(ii) The number of elements,

(iii) Write the elements a13, a21, a33, a24, a23.

**Question 2. **If a matrix has 24 elements, what are the possible orders it can have? What, if it
has 13 elements?

**Question 3.** If a matrix has 18 elements, what are the possible orders it can have? What, if it
has 5 elements?

**Question 4. **Construct a 2 × 2 matrix, A = [aij], whose elements are given by:

(i)
( )2
ij 2
a i j
+
=

(ii) ij
a i
j
=

(iii)
( 2 )2
ij 2
a i j
+
=

**Question 5.** Construct a 3 × 4 matrix, whose elements are given by:

(i)
1| 3 |
ij 2 a = − i + j

(ii) aij = 2i − j

**Question 6.** Find the values of x, y and z from the following equations:

(i)
4 3
5 1 5
y z
x =

(ii)
2 6 2
5 5 8
x y
z xy +

(iii)
9
5
7
x y z
x z
y z + +
+

**Question 7.** Find the value of a, b, c and d from the equation:
2 1 5
2 3 0 13
a b a c
a b c d .

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

(A) m < n

(B) m > n

(C) m = n

(D) None of these

**Question 9. **Which of the given values of x and y make the following pair of matrices equal
3 7 5
1 2 3
x
y x
,
0 2
8 4

(A)
1, 7
3
x y
−
= =

(B) Not possible to find

(C) y = 7,
2
3
x
−
=

(D)
1 , 2
3 3
x y
− −
= =

**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

**Question 19. **A trust fund has Rs 30,000 that must be invested in two different types of bonds.
The first bond pays 5% interest per year, and the second bond pays 7% interest
per year. Using matrix multiplication, determine how to divide Rs 30,000 among
the two types of bonds. If the trust fund must obtain an annual total interest of:

(a) Rs 1800

(b) Rs 2000

**Question 20.** The bookshop of a particular school has 10 dozen chemistry books, 8 dozen
physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60
and Rs 40 each respectively
. Find the total amount the bookshop will receive
from selling all the books using matrix algebra.
Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k,
respectively. Choose the correct answer in Exercises 21 and
22.

**Question 21.** The restriction on n, k and p so that PY + WY will be defined are:

(A) k = 3, p = n

(B) k is arbitrary, p = 2

(C) p is arbitrary, k = 3

(D) k = 2, p = 3

22. If n = p, then the order of the matrix 7X – 5Z is:

(A) p × 2

(B) 2 × n

(C) n × 3

(D) p × n

Choose the correct answer in the Exercises 11 and 12.

**Question 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

**Question 12.** If
cos sin
A ,
sin cos
α − α α α
then A + A′ = I, if the value of α is

(A)
6
π

(B)
3
π

(C) π

(D)
3
2

**Question 10. **A manufacturer produces three products x, y, z which he sells in two markets.
Annual sales are indicated below:
Market Products
I 10,000 2,000 18,000
II 6,000 20,000 8,000

(a) If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively,
find the total revenue in each market with the help of matrix algebra.

(b) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50
paise respectively. Find the gross profit.

**Question 1 1. **Find the matrix X so that
1 2 3 7 8 9
X
4 5 6 2 4 6

**Question 12.** If A and B are square matrices of the same order such that AB = BA, then prove
by induction that ABn = BnA. Further, prove that (AB)n = AnBn for all n ∈ N.
Choose the correct answer in the following questions:

**
Question 13. **If A =
α β
γ α
is such that A² = I, then

(A) 1 + α² + βγ = 0

(B) 1 – α² + βγ = 0

(C) 1 – α² – βγ = 0

(D) 1 + α² – βγ = 0

**Question 14. **If the matrix A is both symmetric and skew symmetric, then
(A) A is a diagonal matrix (B) A is a zero matrix

(C) A is a square matrix

(D) None of these

**Question 15.** If A is square matrix such that A2 = A, then (I + A)³ – 7 A is equal to

(A) A

(B) I – A

(C) I

(D) 3A

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- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 6 Application of Derivatives
- Chapter 7 Integral
- Chapter 8 Application of Integrals
- Chapter 9 Differential Equations
- Chapter 10 Vector Algebra
- Chapter 11 Three Dimensional Geometry
- Chapter 12 Linear Programming
- Chapter 13 Probability

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