# NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1

Get here 12th Maths Exercise 4.1 solutions in PDF file format. NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants in Hindi Medium as well as English Medium are given below. These solutions are useful for CBSE, Uttarakhand, Bihar Board, MP Board, UP Board students who are using NCERT Books for their board exams 2020-2021. UP Board Students are using the same books for Maths as the CBSE Students. So, they can take help to solve Exercise 4.1 of 12th Maths. Download here the UP Board Solutions for 12th Maths Exercise 4.1 in Hindi Medium. Questions related to Exercise 4.1 are solved using the suitable properties and formulae.

The 2×2 determinants can be solved directly but the proper expansion is given for a 3×3 determinants solutions. Videos related to each question are also given for better understanding of concepts.

## NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1

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

Chapter 4: | Exercise 4.1 |

### 12th Maths Exercise 4.1 Solutions

NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants in English as well as Hindi Medium to study online as well as download in PDF for academic session 2020-2021. Download NCERT Books 2020-21 and other supporting material based on latest CBSE Syllabus. Download UP Board Solutions for 12th Maths Chapter 4 Determinants here. Visit to discussion forum to ask your doubts related to NIOS board as well as CBSE Board.

### Class 12 Maths Exercise 4.1 Solutions in Hindi & English

#### Class 12 Maths Exercise 4.1 Question 1, 2, 3, 4, 5 in Video

#### Class 12 Maths Exercise 4.1 Question 5, 6, 7, 8 in Video

#### Class 12 Maths Exercise 4.1 Solution in Hindi Videos

#### Class 12 Maths Exercise 4.1 Question 8 Solution

#### How to solve Determinants?

To solve any determinant, we can expand it through any row R or column C. The result of the determinant is independent of it’s expansion through row or column. If any determinant or order n is multiplied by a real number k, the value of determinant become, k^n times the value of determinant.

##### सारणिकों को हल करना

प्रत्येक सारणिक को हम किसी भी स्तंभ के अनुदिश या फिर किसी भी पंक्ति के अनुदिश प्रसरण करके प्राप्त कर सकते हैं। सरणिक के मान पर किसी पंक्ति या स्तम्भ विशेष का कोई प्रभाव नहीं होता है अर्थात सभी से समान मान प्राप्त होता है। यदि n कोटि वाले किसी सरणिक को किसी संख्या विशेष k से से गुना किया जाए तो उसका मान k^n गुना हो जाता है।

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##### What is a Determinant?

To every square matrix A = [aij] of order n, we can associate a number (real or complex) called determinant of the square matrix A, where aij = (i, j)th element of A.

##### What is the use of Determinants?

Determinants have wide applications in Engineering, Science, Economics, Social Science, etc.

##### How do we find the determinant of a matrix of order 3 × 3?

Determinant of a matrix of order three can be determined by expressing it in terms of second order determinants. This is known as expansion of a determinant along a row (or a column). There are six ways of expanding a determinant of order 3 corresponding to each of three rows (R1, R2 and R3) and three columns (C1, C2 and C3) giving the same value.

##### How can we make the determinant expansion easier?

For easier calculations, we shall expand the determinant along that row or column which contains maximum number of zeros.