NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths 4 Determinants Ex 4.4.

Board	CBSE
Textbook	NCERT
Class	Class 12
Subject	Maths
Chapter	Chapter 4
Chapter Name	Determinants
Exercise	Ex 4.4
Number of Questions Solved	5
Category	NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

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

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

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
$\Delta =\left| \begin{matrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{matrix} \right|$
NCERT Solutions for Class 12 Maths Chapter 4 Determinants 3

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

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.

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

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