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NCERT Solutions for Class 12 Maths Chapter 4 – Determinants Exercise 4.4

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Chapter 4 – Determinants Exercise 4.4

1.

Evaluate determinant using cofactor expansion – Q1 Exercise 4.4

Basic determinant solved with cofactor expansion – Answer Q1

2

Find value of determinant by expanding along row – Q2 Determinants

Step-by-step cofactor method to solve – Q2 sub-question-1

complete expansion – Answer Q2-sub-question-2

3.

Use cofactor method to simplify matrix – Q3

Initial matrix setup for determinant – Q3-sub-question-1

Determinant value derived after simplification – Q3 sub-qstn-2

4.

Expand 3x3 matrix determinant fully – Q4 Class 12

First row expansion applied – Q4 Answer Step 1

Algebraic expression simplification – Q4 Answer Step 2

Intermediate calculations in matrix – Q4 step-3

Final simplified determinant value – Answer Q4 step-4

5.

Simplify determinant with row operations – Q5

Quick determinant solution using identity – Q5 Answer

6.

Determinant problem using properties – Q6 Exercise 4.4

7.

Apply row transformations to solve determinant – Q7

Row manipulation shown clearly – Q7 Answer 1

8.

Verify determinant using row/column changes – Q8 NCERT

Matrix expanded with minor adjustments – Q8 step-1

Property used to simplify terms – Q8 step-2

9.

Use matrix properties to simplify determinant – Q9

Initial determinant approach using column ops – Q9 Part 1

Final determinant value – Answer Q9 Part 3

10.

Determinant problem using identity matrix – Q10

Matrix simplified using row interchange – Q10 sub-1

determinant calculation result – Q10 sub-3

11.

Solve Determinants Class 12 NCERT Exercise 4.4 – Q11 by replacing rows

Apply determinant rules on transformed matrix – Determinants Class 12 NCERT Exercise 4.4-Q11 Step 1

Matrix further simplified – Determinants Class 12 NCERT Exercise 4.4 Q11 Answer 2

Answer derived from identity matrix Determinants Class 12 NCERT Exercise 4.4– Q11

12.

Expand determinant with algebraic terms – Q12 Class 12 NCERT Exercise 4.4

Detailed steps showing matrix expansion – Determinants Class 12 NCERT Exercise 4.4 Q12 step-1

Algebraic manipulation of terms – Determinants Class 12 NCERT Solutions Exercise 4.4 Q12 Answer step-2

Expression simplified to basic form – Determinants Class 12 NCERT Solutions Exercise 4.4 step-3

Continued calculations for Determinants Class 12 NCERT Exercise 4.4– Q12 Part 4

Final solution presented clearly – Determinants Class 12 NCERT Exercise 4.4 Q12-Answer

13.

Evaluate 3x3 determinant with variables – Determinants Class 12 NCERT Exercise 4.4-Q13

Solve determinant with variable coefficients – Determinants Class 12 NCERT Exercise 4.4 Q13 step-1

Step-by-step simplification – Determinants Class 12 NCERT Exercise 4.4 Q13 step-2 Answer

14.

Use transformation to solve Determinants Class 12 NCERT Exercise 4.4– Q14

Initial prep and row operation – Determinants Class 12 NCERT Exercise 4.4-Q14 Answer 1

Determinant value computed – Answer Determinants Class 12 NCERT Exercise 4.4 Q14 answer-2

15.

Determinants Class 12 NCERT Exercise 4.4 simplification with common factors – Q15

Matrix properties applied for simplification – Determinants Class 12 NCERT Exercise 4.4-Q15 Step 1

Further reduction of matrix expression –Determinants Class 12 NCERT Exercise 4.4 Q15 Step 2

Row factorization used – Determinants Class 12 NCERT Exercise 4.4 Q15 step3

value obtained using properties – Determinants Class 12 NCERT Exercise 4.4Q15 step-4

16.

Matrix determinant using addition of rows –Determinants Class 12 NCERT Exercise 4.4 Q16

Matrix simplified by adding rows – Determinants Class 12 NCERT Exercise 4.4 Q16 Step 1

Algebraic transformation in matrix – Determinants Class 12 NCERT Exercise 4.4Q16 Answer-2

More row simplification applied – Determinants Class 12 NCERT Exercise 4.4 Q16 Step 3

determinant value – Determinants Class 12 NCERT Exercise 4.4 Q16 step 4-Answer

17.

Basic determinant simplification – Q17 Exercise 4.4

Quick determinant computation – Answer Q17

18.

Evaluate determinant with row swaps – Q18 Class 12

Apply row operations to matrix – Q18 Part 1

Download Exercise 4.4 NCERT Solutions PDF

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Download Chapter 4 – Determinants NCERT Solutions PDF

Class 12 Maths Chapter 4 – Determinants: All Exercises

Exercise	Link
Exercise 4.1	View Solutions
Exercise 4.2	View Solutions
Exercise 4.3	View Solutions
Exercise 4.5	View Solutions

Class 12 Determinants – Exercise 4.4 Overview

Determinants Class 12 NCERT Solutions Exercise 4.4 helps you to get closer to understanding the use of determinants in linear equation solving. This exercise teaches how determinants become helpful in systems of equations and real-world problem-solving in addition to numerical crunching.

Working through the Chapter 4 Class 12 NCERT Solutions Exercise 4.4 will help you to understand how to use the adjoint method and inverse of a matrix to identify solutions. Common applications in fields like economics, engineering, data analysis, and computer science, these techniques constitute the backbone of linear algebra.

This exercise is fantastic in how it combines useful application with earlier ideas like matrix operations and determinant characteristics. It sharpens your conceptual clarity and gets you ready for challenging tasks sometimes found on tests like JEE.

Determinants Class 12 NCERT Solutions Ex 4.4 lets students apply matrix theory practically. The issues in this exercise exactly coincide with the revised syllabus for 2025. Learners improve their grasp of adjoint procedures it is a must-practice tool whether your preparation for boards or JEE is related.

FAQs – Determinants Class 12 Exercise 4.4 NCERT

Exercise 4.4 use which technique to solve linear equations?

Determinants allow one to solve systems of linear equations using the adjoint method—also known as Cramer’s Rule.

Why is here the determinant of the coefficient matrix significant?

Using this approach, the coefficient matrix’s determinant must be non-zero if a unique solution is to arise.

What is the outcome if the determinant is zero?

A non-unique or inconsistent system is the state of affairs should the determinant be zero: either no solution or infinitely many solutions.

How would I find out whether my answer is accurate?

To confirm whether the solution values satisfy every equation, you can re-enter them back into the original equations.

I think the math is too long. Any suggestions to make things easier?

Absolutely! Try initially solving smaller sections; practice simplifying determinants using properties. Organizing stages and writing cleanly also greatly assist.

Where can I get thorough, methodically detailed explanations?

Go to Cogniks.com for easy explanations and solved examples of full Determinants Class 12 NCERT Solutions Exercise 4.4.