NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4: This page consist of detail and accurate NCERT Solutions For Class 12 Maths Chapter 4-Determinants Exercise 4.4 prepared as per the requirements of CBSE board.
Krati Saraswat16 Jan, 2024
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NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 Determinants is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercises of Chapter 4. Given below is the step by step solutions of all questions given in NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4.NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 Overview
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 addresses these significant subjects. In order to fully comprehend the concepts presented in the chapter and make effective use of the provided solutions, it is recommended that students go over each topic in great detail. The intention is for students to effortlessly achieve excellent exam scores after reviewing and practicing these responses.NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 PDF
We have created comprehensive solutions for NCERT Class 12 Maths, Chapter 4 in order to assist students in comprehending and applying chapter concepts. These questions are meant to help students understand explanations more easily. To download the NCERT Solutions for Class 12 Maths, Chapter 4 PDF, click the following link:NCERT Solutions Class 12 Maths Chapter 4 PDF Download Link
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NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4
Solve The Following Questions NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 Determinants
Question 1. Write minors and cofactors of the elements of the following determinants: (i)
(ii)
Solution :
(i) Let
Minor of element
a
ij
is M
ij.
∴M
11
= minor of element
a
11
= 3
M
12
= minor of element
a
12
= 0
M
21
= minor of element
a
21
= −4
M
22
= minor of element
a
22
= 2
Cofactor of
a
ij
is A
ij
= (−1)
i + j
M
ij
.
∴A
11
= (−1)
1+1
M
11
= (−1)
2
(3) = 3
A
12
= (−1)
1+2
M
12
= (−1)
3
(0) = 0
A
21
= (−1)
2+1
M
21
= (−1)
3
(−4) = 4
A
22
= (−1)
2+2
M
22
= (−1)
4
(2) = 2
(ii) Let
Minor of element
a
ij
is M
ij
.
∴M
11
= minor of element
a
11
=
d
M
12
= minor of element
a
12
=
b
M
21
= minor of element
a
21
=
c
M
22
= minor of element
a
22
=
a
Cofactor of
a
ij
is A
ij
= (−1)
i + j
M
ij.
∴A
11
= (−1)
1+1
M
11
= (−1)
2
(
d
) =
d
A 12 = (−1) 1+2 M 12 = (−1) 3 ( b ) = − b
A 21 = (−1) 2+1 M 21 = (−1) 3 ( c ) = − c A 22 = (−1) 2+2 M 22 = (−1) 4 ( a ) = a
Solution :
A
11
= cofactor of
a
11
= (−1)
1+1
M
11
= 1
A
12
= cofactor of
a
12
= (−1)
1+2
M
12
= 0
A
13
= cofactor of
a
13
= (−1)
1+3
M
13
= 0
A
21
= cofactor of
a
21
= (−1)
2+1
M
21
= 0
A
22
= cofactor of
a
22
= (−1)
2+2
M
22
= 1
A
23
= cofactor of
a
23
= (−1)
2+3
M
23
= 0
A
31
= cofactor of
a
31
= (−1)
3+1
M
31
= 0
A
32
= cofactor of
a
32
= (−1)
3+2
M
32
= 0
A
33
= cofactor of
a
33
= (−1)
3+3
M
33
= 1
A
11
= cofactor of
a
11
= (−1)
1+1
M
11
= 11
A
12
= cofactor of
a
12
= (−1)
1+2
M
12
= −6
A
13
= cofactor of
a
13
= (−1)
1+3
M
13
= 3
A
21
= cofactor of
a
21
= (−1)
2+1
M
21
= 4
A
22
= cofactor of
a
22
= (−1)
2+2
M
22
= 2
A
23
= cofactor of
a
23
= (−1)
2+3
M
23
= −1
A
31
= cofactor of
a
31
= (−1)
3+1
M
31
= −20
A
32
= cofactor of
a
32
= (−1)
3+2
M
32
= 13
A
33
= cofactor of
a
33
= (−1)
3+3
M
33
= 5
Solution :
We know that Δ is equal to the sum of the product of the elements of the second row with their corresponding cofactors.
∴Δ =
a
21
A
21
+
a
22
A
22
+
a
23
A
23
= 2(7) + 0(7) + 1(−7) = 14 − 7 = 7
Solution :
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | |
and A
ij
is Cofactors of
a
ij
, then value of Δ is given by
Solution :
We know that:
Δ = Sum of the product of the elements of a column (or a row) with their corresponding cofactors
∴Δ =
a
11
A
11
+
a
21
A
21
+
a
31
A
31
Hence, the value of Δ is given by the expression given in alternative
D
.
Option (D) is correct.
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4 FAQs
Are there any real-life applications of determinants covered in Exercise 4.4?
Determinants have real-life applications in various fields, and Exercise 4.4 might include problems related to these applications. For example, determinants are used in physics, economics, and engineering to model and solve practical problems.
How can I check if my answers in Exercise 4.4 are correct?
Check your answers using the properties of determinants, especially if the exercise involves manipulations and simplifications. If possible, refer to your textbook or class solutions for verification.
What are the common mistakes to avoid in Exercise 4.4?
Common mistakes may include errors in determinant calculations, misapplication of Cramer's rule, and not following the correct steps in solving problems. Pay attention to the details, double-check your work, and seek clarification if needed.
Can I use matrices to simplify determinants in Exercise 4.4?
Matrices are often used to represent determinants compactly. In the context of Exercise 4.4, matrices might be involved in expressing systems of linear equations and applying methods like Cramer's rule.
How is Cramer's rule applied in Exercise 4.4?
Cramer's rule is a method for solving a system of linear equations using determinants. In Exercise 4.4, you may be asked to apply Cramer's rule to find the solutions of a system of linear equations using determinants.
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