You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2

11th Maths Exercise 7.2 Question 1.
Without expanding the determinant, prove that11th Maths Exercise 7.2 Samacheer Kalvi Chapter 7 Matrices And Determinants
Solution:
11th Maths Exercise 7.2 Answers Samacheer Kalvi Chapter 7 Matrices And Determinants

11th Maths Exercise 7.2 Answers Question 2.
Show that Matrices And Determinants Class 11 Solutions Pdf Samacheer Kalvi Chapter 7 Ex 7.2
Solution:
Matrices And Determinants Class 11 State Board Solutions Samacheer Kalvi Chapter 7 Ex 7.2
11th Maths Matrices And Determinants Solutions Samacheer Kalvi Chapter 7 Ex 7.2

Matrices And Determinants Class 11 Solutions Pdf Question 3.
Prove that 11th Maths Exercise 7.2 In Tamil Samacheer Kalvi Chapter 7 Matrices And Determinants
Solution:
LHS
Taking a from C1, b from C2 and c from C3 we get
11th Maths Determinants Solutions Samacheer Kalvi Chapter 7 Ex 7.2
Expanding along R1 we get
(2c) (abc) (1) [ab + ab] = abc (2c) (2ab)
1 = (abc) (4abc) = 4a2b2c2
= RHS

Matrices And Determinants Class 11 State Board Solutions Question 4.
11th Maths Exercise 7.2 Samacheer Kalvi Chapter 7 Matrices And Determinants
Solution:
11th Maths Matrix Solutions Samacheer Kalvi Chapter 7 Matrices And Determinants Ex 7.2

11th Maths Matrices And Determinants Solutions Question 5.
Prove that Exercise 7.2 Class 11 Maths Solutions State Board Samacheer Kalvi Chapter 7 Matrices And Determinants
Solution:
11th Maths Matrix And Determinants Samacheer Kalvi Chapter 7 Ex 7.2

11th Maths Exercise 7.2 In Tamil Question 6.
Show that 11th Maths Ex 7.2 Samacheer Kalvi Chapter 7 Matrices And Determinants
Solution:
Exercise 7.2 Class 11 Maths Solutions Chapter 7 Matrices And Determinants Samacheer Kalvi
11th Std Maths Determinants Solutions Samacheer Kalvi Chapter 7 Ex 7.2

11th Maths Determinants Solutions Question 7.
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0.
Solution:
11th Maths Book Volume 2 Chapter 7 Samacheer Kalvi Matrices And Determinants Ex 7.2

11th Maths Exercise 7.2 Samacheer Kalvi Question 8.
Class 11 Maths Exercise 7.2 Solutions Samacheer Kalvi Chapter 7 Matrices And Determinants
Solution:
Matrices And Determinants Class 11 Solutions Samacheer Kalvi Chapter 7 Ex 7.2
we get – (aα2 + 2bα + c) [ac – b2]
So Δ = 0 ⇒ (aα2 + 2bα + c) (ac -b2) = – 0 = 0
⇒ aα2 + 2bα + c = 0 or ac – b2 = 0
(i.e.) a is a root of ax2 + 2bx + c = 0
or ac = b2
⇒ a, b, c are in G.P.

11th Maths Matrix Solutions Question 9.
Prove that Matrices And Determinants Class 11 Exercise Samacheer Kalvi Chapter 7 Ex 7.2
Solution:
Determinants Class 11 State Board Solutions Samacheer Kalvi Ex 7.2
11th Maths Matrices And Determinants Pdf Samacheer Kalvi Ex 7.2

Exercise 7.2 Class 11 Maths Solutions State Board Question 10.
If a, b, c are pth, qth and rth terms of an A.P., find the value of Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 21
Solution:
We are given a = tp,b = tq and c = tr
Let a be the first term and d be the common difference
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 22

11th Maths Matrix And Determinants Question 11.
Show that Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 23 is divisible by x4
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 24
Multiplying R1 by a, R2 by b and R3 by c and
taking out a from C1 b from C2 and c from C3 we get
=Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 25=

11th Maths Ex 7.2 Question 12.
If a, b, c are all positive, and are pth, qth and rth terms of a G.P., show that
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 26
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 27
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 28

Exercise 7.2 Class 11 Maths Solutions Question 13.
Find the value of Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 29 if x, y, z ≠ 1.
Solution:
Expanding the determinant along R1
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 30

11th Std Maths Determinants Solutions Question 14.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 31
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 32
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 33

11th Maths Book Volume 2 Chapter 7 Question 15.
Without expanding, evaluate the following determinants:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 34
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 35

10th Maths Exercise 7.2 Samacheer Kalvi Question 16.
If A is a square matrix and |A| = 2, find the value of |AAT|.
Solution:
|A| = 2 (Given) |AT| = 2
Now |AAT| = |A| |AT| = 2 × 2 = 4.

12th Maths Exercise 7.2 Samacheer Kalvi Question 17.
If A and B are square matrices of order 3 such that |A| = -1 and |B| = 3, find the value of |3AB|.
Solution:
Given |A| = -1 : |B| = 3
Given A and B are square matrices of order 3.
∴ |kAB| = k3 |AB|
Here k = 3 ∴ |3AB| = 33 |AB|
= 27 |AB|
= 27 (-1) (3)
= -81

Class 11 Maths Exercise 7.2 Solutions Question 18.
If λ = -2, determine the value of Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 36
Solution:
Given λ = -2
∴ 2λ = -4; λ2 = (-2)2; 3λ2 + 1 = 3 (4) + 1 = 13
6λ – 1 = 6(-2) – 1 = -13
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 37
expanding along R1
0(0) + 4 (0 + 13) + 1 (-52 + 0) = 52 – 52 = 0
Aliter: The determinant value of a skew-symmetric matrix is zero

Matrices And Determinants Class 11 Solutions Question 19.
Determine the roots of the equation Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 38
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 39

Given the determinant value is 0
⇒ 30(1 + x) (2 – x) = 0
⇒ 1 + x = 0 or 2 – x = 0
⇒ x = -1 or x = 2
So, x = -1 or 2.

Matrices And Determinants Class 11 Exercise Question 20.
Verify that det (AB) = (det A) (det B) for Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 40
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 41
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 42
{(-20)(52) (-19) + (10)(38)(—49) + (2)(64)(-17)} – {(-49)(52) (2) + (-17)(38)(-20) + (-19)(64)(10)}
= (19760 – 18620 – 2176) – (-5096 + 12920 – 12160)
= (19760 + 5096 + 12160) – (18620 + 2176 + 12920)
= 37016 – 33716 = 3300 ….(3)
Now (1) × (2) = (3)
(i.e.,) (-33) (-100) = 3300
⇒ det (AB) = (det A), (det B)

Determinants Class 11 State Board Solutions Question 21.
Using cofactors of elements of second row, evaluate |A|, where Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 43
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 44

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 Additional Problems

Exercise 7.2 Class 10 Samacheer Kalvi Question 1.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 45
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 46
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 47

11th Maths Matrices And Determinants Pdf Question 2.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 48
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 49

Question 3.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 50
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 51
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 52

Question 4.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 53
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 54
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 55
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 56

Question 5.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 57
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 58

Question 6.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 59
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 60
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 61

Question 7.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 62
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 63

Question 8.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 64
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 65
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 66

Question 9.
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 67
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 68
Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 69

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