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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 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

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 Ex 4.4 Q1.1

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 Ex 4.4 Q2.1
NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 Q2.2
NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 Q2.3

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|
NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 Q3.1

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 Ex 4.4 Q4.1

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.

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