Example 16 - Chapter 4 Class 12 Determinants

Last updated at December 16, 2024 by Teachoo

Example 16 - Solve system of equations 2x + 5y = 1 3x+2y=7 - Examples part 2 - Example 16 - Examples - Serial order wise - Chapter 4 Class 12 Determinants part 3 - Example 16 - Examples - Serial order wise - Chapter 4 Class 12 Determinants part 4 - Example 16 - Examples - Serial order wise - Chapter 4 Class 12 Determinants

Next: Example 17 Important → Share on WhatsApp

🎉 Smart choice! You just saved 2+ minutes of ads and got straight to the good stuff. That's what being a Teachoo Black member is all about.

Transcript

Example 16 Solve the system of equations 2x + 5y = 1 3x + 2y = 7 Step 1 Write equation as AX = B [■8(2&5@3&2)] [■8(𝑥@𝑦)] = [■8(1@7)] A = [■8(2&5@3&2)] , X = [■8(𝑥@𝑦)] , B = [■8(1@7)] Step 2 Calculate |A|, A = [■8(2&5@3&2)] |A| = |■8(2&5@3&2)| = 2 × 2 – 5 × 3 = 4 – 15 = – 11 Since |𝑨| ≠ 0, System is consistent and the system of equations has a unique solution AX = B X = A-1 B Step 3 Calculating X = A-1 B Here, A-1 = 1/(|A|) adj (A) adj A = [■8(2&5@3&2)] = [■8(2&−5@−3&2)] Now, A-1 = 1/(|A|) adj A Putting values = 𝟏/(−𝟏𝟏) [■8(𝟐&−𝟓@−𝟑&𝟐)] & B = [■8(1@7)] Now X = A-1 B [■8(𝑥@𝑦)] = (−1)/11 [■8(2&−5@−3&2)] [■8(1@7)] [■8(𝑥@𝑦)] = (−1)/11 [■8(2(1)+(⤶7−5)7@−3(1)+2(7))] [■8(𝑥@𝑦)] = (−1)/11 [■8(2−35@−3+14)] = (−1)/11 [■8(−33@11)] = [■8(−33 × (−1)/11@11 × (−1)/11)] [■8(𝑥@𝑦)] = [■8(3@−1)] Hence x = 3 & y = – 1

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular