NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

Get Free NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Determinants Exercise 4.4 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 4 Class 12 Determinants Ex 4.4 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

The topics and sub-topics included in the Determinants chapter are the following:

Section Name	Topic Name
4	Determinants
4.1	Introduction
4.2	Determinant
4.3	Properties of Determinants
4.4	Area of a Triangle
4.5	Adjoint and Inverse of a Matrix
4.6	Applications of Determinants and Matrices
4.7	Summary

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

Ex 4.4 Class 12 Maths Question 1.
Write the minors and cofactors of the elements of following determinants:
(i) $\begin{vmatrix} 2 & -4 \\ 0 & 3 \end{vmatrix}$
(ii) $\begin{vmatrix} a & c \\ b & d \end{vmatrix}$
Solution:
(i) Let A = $\begin{vmatrix} 2 & -4 \\ 0 & 3 \end{vmatrix}$
M₁₁ = 3, M₁₂ = 0, M₂₁ = – 4, M₂₂= 2
For cofactors
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 1

Ex 4.4 Class 12 Maths Question 2.
Write Minors and Cofactor of elements of following determinant
(i) $\left| \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix} \right|$
(ii) $\left| \begin{matrix} 1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2 \end{matrix} \right|$
Solution:
(i) Minors M₁₁ = $\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix}$ = 1
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 2

Ex 4.4 Class 12 Maths Question 3.
Using cofactors of elements of second row, evaluate
$\Delta =\left| \begin{matrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{matrix} \right|$
Solution:
Given
$\Delta =\left| \begin{matrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{matrix} \right|$
tiwari academy class 12 maths Chapter 4 Determinants 3

Ex 4.4 Class 12 Maths Question 4.
Using Cofactors of elements of third column, evaluate
$\Delta =\left| \begin{matrix} 1 & x & yz \\ 1 & y & zx \\ 1 & z & xy \end{matrix} \right|$
Solution:
Elements of third column are yz, zx, xy
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 4

Ex 4.4 Class 12 Maths Question 5.
If $\Delta =\left| \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right|$ and Aij is the cofactors of aij? then value of ∆ is given by
(a) a₁₁A₃₁+a₁₂A₃₂+a₁₃A₃₃
(b) a₁₁A₁₁+a₁₂A₂₁+a₁₃A₃₁
(c) a₂₁A₁₁+a₂₂A₁₂+a₂₃A₁₃
(d) a₁₁A₁₁+a₂₁A₂₁+a₃₁A₃₁
Solution:
Option (d) is correct.