Examples

Chapter 4 Class 12 Determinants
Serial order wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Example 19 Use product [■8(1&−1&[email protected]&2&−[email protected]&−2&4)] [■8(−2&0&[email protected]&2&−[email protected]&1&−2)] to solve the system of equations x – y + 2z = 1 2y – 3z = 1 3x – 2y + 4z = 2 Consider the product [■8(1&−1&[email protected]&2&−[email protected]&−2&4)] [■8(−2&0&[email protected]&2&−[email protected]&1&−2)] =[■8(1(⤶7−2)+(⤶7−1)(9)+2(6)&1(0)+(−1)(2)+2(1)&1(1)+(−1)(−3)+2(−2)@0(−2)+2(9)+(−3)(6)&0(0)+2(2)+(−3)(1)&0(1)+0(−3)+(−3)(−2)@3(−2)+(−2)(9)+(6)&3(0)+(−2)(2)+4(1)&3(1)+(−2)(−3)+4(−2))] = [■8(−2−9+12&0−2+2&1+3−[email protected]+18−18&0+4−3&0−6+6@−6−18+24&0−4+4&3+6−8)] = [■8([email protected]@0)" " ■8([email protected]@0)" " ■8([email protected]@1)] We know that AA-1 = I So [■8(−2&0&[email protected]&2&−[email protected]&1&−2)] is inverse of [■8(1&−1&[email protected]&2&−[email protected]&−2&4)] i.e. [■8(𝟏&−𝟏&𝟐@𝟎&𝟐&−𝟑@𝟑&−𝟐&𝟒)]^(−𝟏)= [■8(−𝟐&𝟎&𝟏@𝟗&𝟐&−𝟑@𝟔&𝟏&−𝟐)] Given equations are x – y + 2z = 1 2y – 3z = 1 3x – 2y + 4z = 2 Writing the equation as AX = B [■8(1&−1&[email protected]&2&−[email protected]&−2&4)] [■8(𝑥@𝑦@𝑧)] = [■8([email protected]@2)] Here A [■8(1&−1&[email protected]&2&−[email protected]&−2&4)], X = [■8(𝑥@𝑦@𝑧)] & B = [■8([email protected]@2)] Now, AX = B X = A-1 B Here A = [■8(1&−1&[email protected]&2&−[email protected]&−2&4)] So, A-1 = [■8(1&−1&[email protected]&2&−[email protected]&−2&4)]^(−1)= [■8(−2&0&[email protected]&2&−[email protected]&1&−2)] Now, X = A-1 B Putting Value [■8(𝑥@𝑦@𝑧)] = [■8(−2&0&[email protected]&2&−[email protected]&1&−2)] [■8([email protected]@2)] = [■8(−2&0&[email protected]&2&−[email protected]&1&−2)] [■8([email protected]@2)] (Calculated above) [■8(𝑥@𝑦@𝑧)] = [■8(−2(1)+0(1)+1(2)@9(1)+2(1)−3(2)@6(1)+1(1)−2(2))] [■8(𝑥@𝑦@𝑧)] =[■8(−[email protected]+2−[email protected]+1−4)] [■8(𝑥@𝑦@𝑧)] = [■8([email protected]@3)] Hence, x = 0 , y = 5 & z = 3

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.