Exercise 1.1 - Chapter 1 - Matrices and Determinants - 11th Business Maths Guide Samacheer Kalvi Solutions

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Chapter 1- Matrices and Determinants - 11th Business Maths Guide Samacheer Kalvi Solutions - Text Book Back Questions and Answers

1.1 Text Book Back Questions and Answers

Question 1.
Find the minors and cofactors of all the elements of the following determinants.

Minor of 5 = M₁₁ = -1
Minor of 20 = M₁₂ = 0
Minor of 0 = M₂₁ = 20
Minor of -1 = M₂₂ = 5
Cofactor of 5 = A₁₁ = (-1)¹⁺¹ M₁₁ = 1 × -1 = -1
Cofactor of 20 = A₁₂ = (-1)¹⁺² M₁₂ = -1 × 0 = 0
Cofactor of 0 = A₂₁ = (-1)²⁺¹ M₂₁ = -1 × 20 = -20
Cofactor of -1 = A₂₂ = (-1)²⁺² M₂₂ = 1 × 5 = 5

Cofactor of 1 is A₁₁ = (-1)¹⁺¹ M₁₁ = -12
Cofactor of -3 is A₁₂ = (-1)¹⁺² M₁₂ = -2
Cofactor of 2 is A₁₃ = (-1)¹⁺³ M₁₃ = 23
Cofactor of 4 is A₂₁ = (-1)²⁺¹ M₂₁ = -1 × -16 = 16
Cofactor of -1 is A₂₂ = (-1)²⁺² M₂₂ = -4
Cofactor of 2 is A₂₃ = (-1)²⁺³ M₂₃ = -14
Cofactor of 3 is A₃₁ = (-1)³⁺¹ M₃₁ = -4
Cofactor of 5 is A₃₂ = (-1)³⁺² M₃₂ = -1 × -6 = 6
Cofactor of 2 is A₃₃ = (-1)³⁺³ M₃₃ = 11

Question 2.

Evaluate 

Solution:

= 3(0 – 2) + 2(6 – 1) + 4(4 – 0)
= -6 + 10 + 16
= 20

Question 3.

Solve:

Solution:

2(7 – 12) – x(28 – 6) + 3(8 – 1) = 0
2(-5) – x(22) + 3(7) = 0
-10 – 22x + 21 = 0
-22x + 11 = 0
-22x = -11

Question 4.
Find |AB| if A =

Solution:

Question 5.

Solve: 

Solution:

7(5 – 3x) – 4(-3 + x²) + 11(-9 + 5x) = 0
35 – 21x + 12 – 4x² – 99 + 55x = 0
-4x² – 21x + 55x + 35 + 12 – 99 = 0
-4x² + 34x – 52 = 0

Divide throughout by -2 we get
2x² – 17x + 26 = 0
(2x – 13) (x – 2) = 0
2x – 13 = 0 (or) x – 2 = 0

Question 6.

Evaluate:

Solution:

Question 7.
Prove that

Solution:

Hence proved.

Question 8.
Prove that

Solution:

= a²b²c² [-(0 – 4) + 0 + 0]
= 4a²b²c²