ML Aggarwal Solutions Class 10 Maths Chapter 8 Matrices

Exercise 8.1


ML Aggarwal Solutions Class 10 Maths Chapter 8 Matrices

ML Aggarwal Solutions Class 10 Maths Chapter 8 Matrices-

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2. (i) If a matrix has 4 elements, what are the possible order it can have? 
Solution: 
We have given that,  
Matrix has 4 elements 
It can have 1 × 4,4 × 1 or 2 × 2 order.
 
(ii) If a matrix has 4 elements, what are the possible orders it can have? 
Solution: 
We have given that, 
Matrix has 4 elements, 
It can have 1 × 8, 8 × 1, 2 × 4 or 4 × 2 order.

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x = 2
Substituting the value of x in (i)
4 + y = 5
y = 5 – 4
y = 1
Hence x = 2 and y = 1
 
 
 
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x = 5 – 3
x = 2
Again we have
y – 4 = 3
y = 3 + 4
y = 7
Hence x = 2 and y = 7
 
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x + 2 = -5
x = -5 – 2
x = -7
Also, we have 5z = -20
z = -20/5
z = – 4
Again from given matrix we have
y2  + y – 6 = 0
The above equation can be written as
y2  + 3y – 2y – 6 = 0
y (y + 3) – 2 (y + 3) = 0
y + 3 = 0 or y – 2 = 0
y = -3 or y = 2
Hence x = -7,y = -3,2 and z = -4
 
 
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x – 2 = 3 and y = 1
x = 2 + 3
x = 5
Again, we have
a + 2b = 5 ... i
3a – b = 1 …ii
Multiply (i) by 1 and (ii) by 2
a + 2b = 5
6a – 2b = 2
Now by adding above equations we get
7a = 7
a =7/7
a = 1
Substituting the value of a in (i) we get
1 + 2b = 5
2b = 5 -1
2b = 4
b =4/2
b = 2
 
 
 
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Comparing the corresponding terms, we get
3 = d
d = 3
Also we have
5 + c = -1
c = -1 – 5
c = -6
Also we have,
a + b = 6 and a b = 8
We know that,
(a – b)2  = (a + b)2  – 4ab
(6)2  – 32 = 36 – 32 = 4 = (± 2)2
a – b = ± 2
If a – b = 2
a + b = 6
Adding the above two equations we get
2a = 4
a =4/2
a = 2
b = 6 – 4
b = 2
Again, we have a – b = -2
 
and a + b = 6
Adding above equations we get
2a = 4
a =4/2
a = 2
Also, b = 6 – 2 = 4
a = 2 and b = 4
 
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Comparing the corresponding terms, we get
3x + 4y = 2 ….i
x – 2y = 4 …..ii
Multiply (i) by 1 and (ii) by 2
3x + 4y = 2
2x – 4y = 8
Adding the above equations we get
5x = 10
x =10/5
x = 2
Substituting the value of x in (i)
We get
6 + 4y = 2
4y = 2 – 6
4y = -4
y = -1
 
Exercise 8.2

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EXERCISE : 8.3


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⇒b(b-1)-2(b-1)=0
⇒(b-1)(b-2)=0
Either b-1=0,
Then, b=1 or b-2=0,
Then, b=2
Hence a=2,b=2 or 1
 
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Now, compare both the elements
3a=4+a 
a-a=4
2a=4
∴ a=2
3b=a+b+6
3b-b=2+6
2b=8
∴b=4
3d=3+2d
3d-2d=3
∴d=3
3c=c+d-1
3c-c=3-1
2c=2
∴c=1
Hence a=2,b=4,c=1 and d=3
 
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ML Aggarwal Solutions Class 10 Maths Chapter 1 Goods and Service Tax (GST)
ML Aggarwal Solutions Class 10 Maths Chapter 2 Banking
ML Aggarwal Solutions Class 10 Maths Chapter 3 Shares and Dividends
ML Aggarwal Solutions Class 10 Maths Chapter 4 Linear Inequations
ML Aggarwal Solutions Class 10 Maths Chapter 5 Quadratic Equations in One Variable
ML Aggarwal Solutions Class 10 Maths Chapter 6 Factorization
ML Aggarwal Solutions Class 10 Maths Chapter 7 Ratio and Proportion
ML Aggarwal Solutions Class 10 Maths Chapter 7 Ratio and Proportion
ML Aggarwal Solutions Class 10 Maths Chapter 8 Matrices
ML Aggarwal Solutions Class 10 Maths Chapter 9 Arithmetic and Geometric Progression
ML Aggarwal Solutions Class 10 Maths Chapter 10 Reflection
ML Aggarwal Solutions Class 10 Maths Chapter 11 Section Formula
ML Aggarwal Solutions Class 10 Maths Chapter 12 Equation of Straight Line
ML Aggarwal Solutions Class 10 Maths Chapter 13 Similarity
ML Aggarwal Solutions Class 10 Maths Chapter 14 Locus
ML Aggarwal Solutions Class 10 Maths Chapter 15 Circles
ML Aggarwal Solutions Class 10 Maths Chapter 16 Constructions
ML Aggarwal Solutions Class 10 Maths Chapter 17 Mensuration
ML Aggarwal Solutions Class 10 Maths Chapter 18 Trigonometric Identities
ML Aggarwal Solutions Class 10 Maths Chapter 19 Trigonometric Tables
ML Aggarwal Solutions Class 10 Maths Chapter 20 Heights and Distances
ML Aggarwal Solutions Class 10 Maths Chapter 21 Measures Of Central Tendency
ML Aggarwal Solutions Class 10 Maths Chapter 22 Probability
NCERT Exemplar Solutions Class 10 Maths Areas related to Circles
NCERT Exemplar Solutions Class 10 Maths Arithmetic Progression
NCERT Exemplar Solutions Class 10 Maths Circles
NCERT Exemplar Solutions Class 10 Maths Construction
NCERT Exemplar Solutions Class 10 Maths Coordinate Geometry
NCERT Exemplar Solutions Class 10 Maths Linear Equations
NCERT Exemplar Solutions Class 10 Maths Polynomials
NCERT Exemplar Solutions Class 10 Maths Quadratic Equation
NCERT Exemplar Solutions Class 10 Maths Real Numbers
NCERT Exemplar Solutions Class 10 Maths Surface Area and Volume
NCERT Exemplar Solutions Class 10 Maths Triangles
NCERT Exemplar Solutions Class 10 Maths Trigonometry