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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 4 |

Exercise | Class 12 Maths Chapter 4 Determinants Exercise 4.4 |

Number of Questions Solved | 5 |

## 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 = $\begin{vmatrix} 2 & -4 \ 0 & 3 \end{vmatrix}$

M_{11} = 3, M_{12} = 0, M_{21} = – 4, M_{22 }= 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 M_{11} = $\begin{vmatrix} 1 & 0 \ 0 & 1 \end{vmatrix}$ = 1

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

**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) a _{11}A_{31}+a_{12}A_{32}+a_{13}A_{33}**

**(b) a**

_{11}A_{11}+a_{12}A_{21}+a_{13}A_{31}**(c) a**

_{21}A_{11}+a_{22}A_{12}+a_{23}A_{13}**(d) a**

_{11}A_{11}+a_{21}A_{21}+a_{31}A_{31}**Solution:**

Option (d) is correct.

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

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