NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 Determinants in Hindi and English Medium for all boards modified for academic session 2023-24. Questions of class 12 Maths ex. 4.5 are revised and updated as per new rationalised NCERT textbooks issued for curriculum 2023-24.

## Class 12 Maths Exercise 4.5 Solutions in Hindi and English

### NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5

UP Board students are now using NCERT textbooks for their board exams. So, they can download UP Board Solutions for 12th Maths Exercise 4.5 form here in PDF format. In exercise 4.5, we will learn, how to check the consistency of the system of linear equation, how do we solve linear equation using matrix and determinants.

Normally, a six marks questions asked from this exercise in CBSE board exams. So, the exercise 4.5 of 12th Maths is one of the important exercises for board exams. Download NCERT Solutions of other subjects updated for new academic session based on new CBSE Curriculum.

Class: 12 | Mathematics |

Chapter 4: | Exercise 4.5 |

Topic: | Determinants |

Session: | 2023-24 |

Content Type: | Images, Text and Videos Format |

Medium: | English and Hindi Medium |

#### 12th Maths Exercise 4.5 Solutions

NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 Determinants in English & Hindi Medium updated for new academic session 2023-24. Exercise 4.5 is basically based on the solutions of linear equations in three variables using adjoint & inverse of a matrix. Download NCERT Books and solutions with offline apps for offline use.

#### Class 12 Maths Exercise 4.5 Question 6, 7 in Video

#### Class 12 Maths Exercise 4.5 Question 8, 9 in Video

#### Class 12 Maths Exercise 4.5 Question 10, 11 in Video

##### About 12 Maths Exercise 4.5

In Exercise 4.5, we have to check whether the given linear equations are consistent or inconsistent. If the equations are consistent, then using Inverse of Matrix, we have to find the value of unknown variable.

In CBSE Class 12, we have to solve the equations containing maximum of three variables but later on we can find the values of variables more than 3 also. Some applications based on Matrix is also given in this exercise.

### Important Questions of 12th Maths Exercise 4.5

### Are all matrices invertible?

No, only square matrices are said to be invertible matrices.

### Is Exercise 4.6 of 12th Maths important as per examination point of view?

A six marks question is asked from Class 12 Maths Exercise 4.6 most of the time in CBSE Exams. The solutions of system of linear equations is the base for the question.

### What is a one to one matrix?

One to one matrix is used in linear transformation. A linear transformation that maps all the distinct points into distinct points is said to be a one-to-one transformation.

### Can you find the determinant of a 3×4 matrix?

No, determinant of matrix can be calculated if it is a square matrix. 3×4 is not a square matrix.

###### HOW TO SOLVE SYSTEM OF LINEAR EQUATIONS

First of all find |A| and then check whether it is consistent or inconsistent. If is is consistent, find the Inverse of A and apply the formula X = A-1B, to find the unknown variables. If |A| = 0, find (adj A).B. If (adj A).B ≠ 0, then there is no solutions of the given system of linear equations. If it is non-zero, there may be no solutions or infinite many solutions.

### How can students score full marks in exercise 4.5 chapter 4 of Class 12th Maths?

Exercise 4.5 of class 12th Maths contains three examples (examples 27, 28, 29) and 16 questions. All questions and examples of this exercise are most important from the exam point of view. So, to score full marks in exercise 4.5 of grade 12th Maths, students should honestly practice these questions and examples. These questions can come in 2 to 6 marks in the board exams.

### How many days are needed to complete exercise 4.5 of grade 12th Maths?

If students can give 2 hours per day to exercise 4.5 of class 12th Maths, they need 3-4 days to complete exercise 4.5 of class 12th Maths. This time is an approximate time. This time can vary because no students can have the same working speed, efficiency, capability, etc.

### Is exercise 4.5 of class 12th Maths easy or tough?

Exercise 4.5 of class 12th Maths is not easy and not tough. It lies in the mid of easy and tough because some examples and questions of this exercise are easy, and some are complex. However, the difficulty level varies from child to child. So, exercise 4.5 of class 12th Maths is easy, or tough depends on children also. Some children find it difficult, some find it easy, and some find it in the middle of easy and difficult.

### When is a system of equations consistent and inconsistent in exercise 4.5 of NCERT 12th Maths?

Consistent system: A system of equations is said to be consistent if its solution (one or more) exists.

Inconsistent system: A system of equations is said to be inconsistent if its solution does not exist.