Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide Solution For R.D. Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 2 sub question 10 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter determinants Exercise 5.2  Question 2 Sub Question 10 Maths Textbook Solution.

Answers (1)

Answer:\left|\begin{array}{llll} 1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2} \end{array}\right|=0

Hint: We will try to do any two column or row equal

Given:\left|\begin{array}{cccc} 1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2} \end{array}\right|

Solution:\left|\begin{array}{cccc} 1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2} \end{array}\right|

\begin{aligned} &\text { On applying } C_{3} \rightarrow C_{3}-C_{2} \text { and } C_{4} \rightarrow C_{4}-C_{1}\\ &=\left|\begin{array}{cccc} 1^{2} & 2^{2} & 3^{2}-2^{2} & 4^{2}-1^{2} \\ 2^{2} & 3^{2} & 4^{2}-3^{2} & 5^{2}-2^{2} \\ 3^{2} & 4^{2} & 5^{2}-4^{2} & 6^{2}-3^{2} \\ 4^{2} & 5^{2} & 6^{2}-5^{2} & 7^{2}-4^{2} \end{array}\right|\\ &=\left|\begin{array}{cccc} 1^{2} & 2^{2} & 9-4 & 16-1 \\ 2^{2} & 3^{2} & 16-9 & 25-4 \\ 3^{2} & 4^{2} & 25-16 & 36-9 \\ 4^{2} & 5^{2} & 36-25 & 49-16 \end{array}\right|\\ &=\left|\begin{array}{cccc} 1^{2} & 2^{2} & 5 & 15 \\ 2^{2} & 3^{2} & 7 & 21 \\ 3^{2} & 4^{2} & 9 & 27 \\ 4^{2} & 5^{2} & 11 & 33 \end{array}\right|\\ &\text { On taking common } 3 \text { from } \mathrm{C}_{4}\\ &=3\left|\begin{array}{cccc} 1^{2} & 2^{2} & 5 & 5 \\ 2^{2} & 3^{2} & 7 & 7 \\ 3^{2} & 4^{2} & 9 & 9 \\ 4^{2} & 5^{2} & 11 & 11 \end{array}\right| \end{aligned}

If any two rows or columns of a determinant are identical.

The value of the determinant is zero

\begin{aligned} &=3 \times 0 \quad\left(\because C_{3}=C_{4}\right) \\ &=0 \end{aligned}

Hence\left|\begin{array}{cccc} 1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2} \end{array}\right|=0

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Single Girl Child Scholarship 2024: Registration extended till January 10; eligibility criteria, amount
anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14

Latest Question