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

These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.4 Questions and Answers are prepared by our highly skilled subject experts. https://mcq-questions.com/ncert-solutions-for-class-12-maths-chapter-4-ex-4-4/

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

Ex 4.4 Class 12 NCERT Solutions  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:

Exercise 4.4 Class 12 NCERT Solutions 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:

4.4 Class 12 NCERT Solutions 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:

Exercise 4.4 Class 12 Maths NCERT Solutions 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:

= yz² – y²z + zx² – xz² + xy² – x²y
= – xz² – zy² + z²y – x²y + x²z + xy²
= xyz – xz²- zy² + z²y – x²y + x²z + xy² – xyz (adding and substracting xyz)
= xz(y – z) – zy(y – z) – x²(y – z) + xy(y – z)
= (xz – zy) (y – z) – (x² – xy)(y – z)
= z(x – y)(y – z) – x(x – y)(y – z)
= (x – y)(y – z)(z – x)

Exercise 4.4 Class 12 Maths Solutions 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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