# NCERT Solutions For Class 12 Maths Chapter 4 Determinants Ex 4.4

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## NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4

NCERT TEXTBOOK EXERCISES

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

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

Ex 4.4 Class 12 Maths Question 3. Using cofactors of elements of second row, evaluate
Δ= $\Delta =\left| \begin{matrix} 5 & 3 & 8 \ 2 & 0 & 1 \ 1 & 2 & 3 \end{matrix} \right|$

Solution:

Given
Δ= $\Delta =\left| \begin{matrix} 5 & 3 & 8 \ 2 & 0 & 1 \ 1 & 2 & 3 \end{matrix} \right|$

Ex 4.4 Class 12 Maths Question 4.

Using Cofactors of elements of third column, evaluate
Δ= $\Delta =\left| \begin{matrix} 1 & x & yz \ 1 & y & zx \ 1 & z & xy \end{matrix} \right|$

Solution:

Elements of third column are yz, zx, xy

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.

## NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.4 PDF

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