ML Aggarwal Matrices Exe-8.1 Class 10 ICSE Maths Solutions

ML Aggarwal Matrices Exe-8.1 Class 10 ICSE Maths Solutions. We Provide Step by Step Answer of  Exe-8.1 Questions for Matrices as council prescribe guideline for upcoming board exam.  Visit official Website CISCE for detail information about ICSE Board Class-10.

ML Aggarwal Matrices Exe-8.1 Class 10 ICSE Maths Solutions

Board	ICSE
Subject	Maths
Class	10th
Chapter-8	Matrices
Writer / Book	Understanding
Topics	Solutions of Exe-8.1
Academic Session	2024-2025

 

Matrices Exe-8.1 Questions

ML Aggarwal Class 10 ICSE Maths Solutions

Page-142

Question-1. Classify the following matrices:

Answer :

(i) It is square matrix of order 2
(ii) It is row matrix of order 1 × 3
(iii) It is column matrix of order 3 × 1
(iv) It is matrix of order 3 × 2
(v) It is matrix of order 2 × 3
(vi) It is zero matrix of order 2 × 3

Question -2

(i) If a matrix has 4 elements, what are the possible order it can have ?
(ii) If a matrix has 8 elements, what are the possible order it can have ?

Answer:

(i) It can have 1 × 4, 4 × 1 or 2 × 2 order
(ii) It can have 1 × 8, 8 × 1,2 × 4 or 4 × 2 order

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Matrices Exe-8.1 Questions

ML Aggarwal Class 10 ICSE Maths Solutions

Page-143

Question -3. Construct a 2 x 2 matrix whose elements a_ij are given by

(i) a_ij = 2i – j
(ii) a_ij = i.j

Answer:

Question -4. Find the values of x and y if :

Answer:

Comparing corresponding elements,
2x + y = 5 …(i)
3x – 2y = 4 …(ii)
Multiply (i) by 2 and (ii) by ‘1’ we get
4x + 2y = 10, 3x – 2y = 4
Adding we get, 7x = 14 ⇒ x = 2
Substituting the value of x in (i)
2 x 2 + y = 5 ⇒ 4 + y = 5
y = 5 – 4 = 1
Hence x = 2, y = 1

Question- 5. Find the value of x if

Answer:

Comparing the corresponding terms, we get.
-y = 2
⇒ y = -2

3x + y = 1

3x = 1 – y

Substituting value of y

3x = 1 – (-2)

3x = 1 + 2

3x = 3

x = 3/3

x = 1

Therefore  x = 1 and y = -2

Question -6

If  ,find values of x and y

Answer:

Comparing the corresponding terms, we get.
x + 3 = 5
⇒ x = 5 – 3 = 2
⇒ y – 4 = 3
⇒ y = 3 + 4 = 7
x = 2, y = 7

Question- 7. Find the values of x, y and z if

Answer:

Comparing the corresponding elements of equal Matrices
x + 2 = -5
⇒ x = -5 – 2 = -7

5z = -20

z = -20/5

z = – 4

y² + y – 6 = 0

y² + 3y – 2y – 6 = 0

y (y + 3) – 2 (y + 3) = 0

y + 3 = 0 or y – 2 = 0

y = -3 or y = 2

So x = -7, y = -3, 2 and z = -4

Question -8. Find the values of x, y, a and b if

Answer:

Comparing corresponding elements
x – 2 = 3, y = 1
x = 3 + 2 = 5
a + 2b = 5 ……(i)
3a – b = 1 ……..(ii)

Multiply (i) by 1 and (ii) by 2

a + 2b = 5 ……(i)

6a – 2b = 2  ……..(ii)

adding both equation

7a = 7

a = 7/7

a = 1

Substituting the value of a in Equ (i)

1 + 2b = 5

2b = 5 -1

2b = 4

b = 4/2

b = 2

Question -9. Find the values of a, b, c and d if

Answer -9

Comparing the corresponding terms, we get.
3 = d ⇒ d = 3
⇒ 5 + c = – 1
⇒ c = -1 – 5
⇒ c = -6
a + b = 6 and ab = 8

Now using (a – b)² = (a + b)² – 4 ab

(6)² – 32 = 36 – 32 = 4 = (± 2)²

a – b = ± 2

If a – b = 2

a + b = 6

Adding the both equations

2a = 4

a = 4/2

a = 2

b = 6 – 4

b = 2

now

a – b = -2

And a + b = 6

Adding  equations

2a = 4

a = 4/2

a = 2

Also, b = 6 – 2 = 4

a = 2 and b = 4

—  : End of ML Aggarwal Matrices Exe-8.1 Class 10 ICSE Maths Solutions :–

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