NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.1 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths 4 Determinants Ex 4.1.
- Determinants Class 12 Ex 4.2
- Determinants Class 12 Ex 4.3
- Determinants Class 12 Ex 4.4
- Determinants Class 12 Ex 4.5
- Determinants Class 12 Ex 4.6
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 12 |
| Subject | Maths |
| Chapter | Chapter 4 |
| Chapter Name | Determinants |
| Exercise | Ex 4.1 |
| Number of Questions Solved | 8 |
| Category | NCERT Solutions |
NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.1
Question 1.
Evaluate the following determinant:
Solution:
= 2x(-1)-(-5)x(4)
=-2+20
=18
Question 2.
(i)
(ii)
Solution:
(i)
= cosθ cosθ – (sinθ)(-sinθ)
= cos²θ + sin²θ
= 1
Question 3.
If 
Solution:
=>
L.H.S = |2A|
=
= – 24
Question 4.
![A=\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{matrix} \right]](http://s0.wp.com/latex.php?latex=A%3D%5Cleft%5B+%5Cbegin%7Bmatrix%7D+1+%26+0+%26+1+%5C%5C+0+%26+1+%26+2+%5C%5C+0+%26+0+%26+4+%5Cend%7Bmatrix%7D+%5Cright%5D+&bg=ffffff&fg=000&s=2 "A=\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{matrix} \right]")
Solution:
3A =
=
![3\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{matrix} \right]](http://s0.wp.com/latex.php?latex=3%5Cleft%5B+%5Cbegin%7Bmatrix%7D+1+%26+0+%26+1+%5C%5C+0+%26+1+%26+2+%5C%5C+0+%26+0+%26+4+%5Cend%7Bmatrix%7D+%5Cright%5D+&bg=ffffff&fg=000&s=2 "3\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{matrix} \right]")
![3\left[ \begin{matrix} 3 & 0 & 3 \\ 0 & 3 & 6 \\ 0 & 0 & 12 \end{matrix} \right]](http://s0.wp.com/latex.php?latex=3%5Cleft%5B+%5Cbegin%7Bmatrix%7D+3+%26+0+%26+3+%5C%5C+0+%26+3+%26+6+%5C%5C+0+%26+0+%26+12+%5Cend%7Bmatrix%7D+%5Cright%5D+&bg=ffffff&fg=000&s=2 "3\left[ \begin{matrix} 3 & 0 & 3 \\ 0 & 3 & 6 \\ 0 & 0 & 12 \end{matrix} \right]")
Question 5.
Evaluate the following determinant:
(i)
(ii)
(iii)
(iv)
Solution:
(i)
Question 6.
If ![\left[ \begin{matrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{matrix} \right]](http://s0.wp.com/latex.php?latex=%5Cleft%5B+%5Cbegin%7Bmatrix%7D+1+%26+1+%26+-2+%5C%5C+2+%26+1+%26+-3+%5C%5C+5+%26+4+%26+-9+%5Cend%7Bmatrix%7D+%5Cright%5D+&bg=ffffff&fg=000&s=2 "\left[ \begin{matrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{matrix} \right]")
Solution:
|A| =
= 1(-9+12)-1(-18+15)-2(8-5)
= 0
Question 7.
Find the values of x, if
(i)
(ii)
Solution:
(i)
=> 2 – 20 = 2x² – 24
=> x² = 3
=> x = ±√3
(ii)
or
2 × 5 – 4 × 3 = 5 × x – 2x × 3
=>x = 2
Question 8.
If 
(a) 6
(b) +6
(c) -6
(d) 0
Solution:
(b)
=> x² – 36 = 36 – 36
=> x² = 36
=> x = ± 6
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