2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6

Students can Download Maths Chapter 4 Determinants Ex 4.6 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6

2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.6

Examine the consistency of the system of equations.

Question 1.
x + 2y = 2
2x + 3y =2
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.1
hence consistence and unique solution.

Question 2.
2x – y = 5
x + y = 4
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.2
hence system is consistent and has unique solution

Question 3.
x + 3y = 5
2x + 6y = 8
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.3

KSEEB Solutions

Question 4.
x + y + z = 1
2x + 3y + 22 = 2
ax + ay + 2az = 4
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.4
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.5

case (i).
If a ≠ 0,
The system is consistent and unique solution
case ii. If a = 0  we can’t say any thing about
consistency
Now we find whether
(Adj A) B is zero or not
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.6

Question 5.
3x – y – 2z = 2
2y – z = -1
3x – 5y = 3
Answer:

2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.7
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.8

KSEEB Solutions

Question 6.
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = -1
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.9

Solve the system of linear equations (7 – 14)

Question 7.
5x + 2y = 4
7x + 3y = 5
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.10
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.11

Question 8.
2x – y = -2
3x + 4y = 3
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.12

Question 9.
4x – 3y = 3
3x – 5y = 7
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.14
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.15

KSEEB Solutions

Question 10.
5x + 2y = 3
3x + 2y = 5
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.16

Question 11.
2x + y + z = 1
x – 2y – z = \(\frac{3}{2}\)
3v – 5z =9
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.17
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.18

KSEEB Solutions

Question 12.
x – y + z = 4
2x + y – 3z = 0
x + y + z = 2
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.19
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.20

Question 13.
2x + 3y + 3z = 5
x – 2y + z = -4
3x – y – 22 = 3
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.21

Question 14.
x – y + 2z = 7
3x + 4y – 5z = -5
2x – y + 3z = 12
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.22

KSEEB Solutions

Question 15.
\(A=\left[\begin{array}{ccc}{2} & {-3} & {5} \\{3} & {2} & {-4} \\{1} & {1} & {-2}\end{array}\right]\) find A-1 using A-1 solve
2x – 3y + 5z = 11
3x + 2y – 4z = -5
x + y – 2z = -3
Answer:
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.23
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.24

Question 16.
The cost of 4 kg onion, 3kg wheat and 2 kg rice is 60/-
The cost of 2 kg onion, 4 kg wheat and 6 kg rice is 90/-­
The cost of 6 kg onion, 2kg wheat and 3kg rice is 70/-
Find the cost of each item per kg by matrix method.
Answer:
Let the cost of onion be ₹ y/-
Let the cost of wheat be ₹x/-
Let the cost of rice be ? ₹ z/-
4x + 3y + 2z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70
AX = B ⇒ X = A-1B
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.25
2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.6.26

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