# NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5

NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 Determinants in Hindi Medium as well as English Medium. Now NCERT Books are being used as textbooks for all the students of CBSE, Uttarakhand, Bihar board, MP Board, UP Board and other board also. So, these solutions are useful not only for CBSE board but UP Board, MP board and all other board who are using NCERT Books. Djownload here the UP Board solutions for Class 12 Maths Chapter 4 Exercise 4.5 in Hindi Medium and English Medium. Solutions are available in PDF format as well as Online study (without downloading). Videos related to all questions of Exercise 4.5

5 of 12th Maths are given below in Hindi and English Medium. Download NCERT Solutions for 2020-21 in updated form for new academic session. Offline apps work without internet once downloaded.## NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5

Class: 12 | Maths (English and Hindi Medium) |

Chapter 4: | Exercise 4.5 |

### 12th Maths Exercise 4.5 Solutions

NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 Determinants English and Hindi Medium free to download for offline use. UP Board Solutions for Class 12 Maths Exercise 4.5 are also same as CBSE Board solutions. In this exercise, you have to learn how to find adjoint of a matrix A and how to find inverse of a square matrix. इस प्रश्नावली में विद्यार्थी किसी भी आव्यूह का सहखंडज निकलना और फिर उसकी मदद से आव्यूह का व्युत्क्रम निकलना सीखते हैं। ताकि आने वाली प्रश्नावली में, रैखिक समीकरणों को हल करते समय इसका प्रयोग कर सकें। Download NCERT Books for Class 12 for Academic Session 2020-2021 for offline use.

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

#### Class 12 Maths Exercise 4.5 Question 1, 2 in Video

#### Class 12 Maths Exercise 4.5 Question 3, 4 in Video

#### Class 12 Maths Exercise 4.5 Question 5, 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

#### Class 12 Maths Exercise 4.5 Question 12, 13 in Video

#### Class 12 Maths Exercise 4.5 Question 14, 15 in Video

#### Class 12 Maths Exercise 4.5 Question 16, 17, 18 in Video

#### Adjoint and Inverse of a Matrix

Adjoint and Inverse of a Matrix is important in finding the solutions of system of linear equation in many variables. During the researches in any field the linear equations of so many variables are formed, then Matrices helps to solve them easily. Adjoint of a matrix of order two can be directly by interchanging a11 & a11 and then changing the sign of a12 & a21.

##### आव्यूह का सहखंडज

कोटि 2 के आव्यूह का सहखंडज प्राप्त करने के लिए अवयव a11 और अवयव a22 को आपस में एक दूसरे से बदल दें। इसके बाद अवयव a12 और अवयव a21 के चिन्हों को बदल दे। अब जो आव्यूह प्राप्त होगा वह दिए गए आव्यूह का सहखंडज होगा। इस प्रकार सीधे बिना किसी गणना के ही सहखंडज निकाल सकते है।

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##### Where does one use determinants in real life?

Determinants can be used in mensuration to find areas and volumes. It is frequently used in research to solve linear equations. Determinants are also used in applied Mathematics.

##### Who initiate the using determinants as a tool in Mathematics?

The Chinese method of representing the coefficients of the unknowns of several linear equations by using rods on a calculating board naturally led to the discovery of simple method of elimination. The arrangement of rods was precisely that of the numbers in a determinant. The Chinese, therefore, early developed the idea of subtracting columns and rows as in simplification of a determinant Mikami, China, pp 30, 93.

##### What are the main properties of determinants?

The main properties of determinants are as follows:

1. If we interchange any two rows (or columns), then sign of determinant changes.

2. If any two rows or any two columns are identical or proportional, then value of determinant is zero.

3. If we multiply each element of a row or a column of a determinant by constant k, then value of determinant is multiplied by k.

4. Multiplying a determinant by k means multiply elements of only one row (or one column) by k.

5. If elements of a row or a column in a determinant can be expressed as sum of two or more elements, then the given determinant can be expressed as sum of two or more determinants.

6. If to each element of a row or a column of a determinant the equimultiples of corresponding elements of other rows or columns are added, then value of determinant remains same.

##### What does a determinant of 1 mean?

When the value of a determinant is 1, the matrix associated to this determinant is said to be unimodular.