Evaluate the product AB, where A =[1 -1 0   2 3 4   0 1 2] and B = [2 2 -4  -4 2 -4  2 -1 5]. Hence the solve system of linear equations

x – y = 3

2x + 3y + 4z = 17

y + 2z = 7

 

Evaluate the product AB, where A = [ 1 −1 0 2 3 4 0 1 2 ] and B = [

Question 36 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2
Question 36 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 3
Question 36 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 4
Question 36 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 5

 

 

Note : This is similar to Example 33 of NCERT – Chapter 4 Class 12 Determinants

Check the answer here https:// www.teachoo.com /3304/694/Example-33---Use-product-to-solve-x-y-2z1-2y-3z1-3x-2y-4z2-/category/Examples/

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Transcript

Question 36 (Choice 2) Evaluate the product AB, where A =[■8(1&−1&0@2&3&4@0&1&2)] and B = [■8(2&2&−4@−4&2&−4@2&−1&5)] Hence the solve system of linear equations x – y = 3 2x + 3y + 4z = 17 y + 2z = 7 Finding the product [■8(1&−1&0@2&3&4@0&1&2)] [■8(2&2&−4@−4&2&−4@2&−1&5)] =[■8(1(2)+(⤶7−1)(−4)+0(2)&1(2)+(−1)(2)+0(−1)&1(−4)+(−1)(−4)+0(5)@2(2)+3(−4)+4(2)&2(2)+3(2)+4(−1)&2(−4)+3(−4)+4(5)@0(2)+1(−4)+2(2)&0(2)+1(2)+2(−1)&0(−4)+1(−4)+2(5))] = [■8(6@0@0)" " ■8(0@6@0)" " ■8(0@0@6)] = 6[■8(1@0@0)" " ■8(0@1@0)" " ■8(0@0@1)] Thus, AB = 6I A × 𝑩/𝟔 = I We know that AA-1 = I So 𝟏/𝟔 [■8(𝟐&𝟐&−𝟒@−𝟒&𝟐&−𝟒@𝟐&−𝟏&𝟓)] is inverse of [■8(1&−1&0@2&3&4@0&1&2)] Given equations are x – y = 3 2x + 3y + 4z = 17 y + 2z = 7 Writing the equation as AX = D [■8(1&−1&2@0&2&−3@3&−2&4)] [■8(𝑥@𝑦@𝑧)] = [■8(3@17@7)] Here A = [■8(1&−1&0@2&3&4@0&1&2)], X = [■8(𝑥@𝑦@𝑧)] & D = [■8(3@17@7)] Now, AX = D X = A-1 D Putting A-1 = 𝟏/𝟔 𝑩=𝟏/𝟔 [■8(𝟐&𝟐&−𝟒@−𝟒&𝟐&−𝟒@𝟐&−𝟏&𝟓)] So, our equation becomes [■8(𝑥@𝑦@𝑧)] = 𝟏/𝟔 [■8(𝟐&𝟐&−𝟒@−𝟒&𝟐&−𝟒@𝟐&−𝟏&𝟓)] [■8(3@17@7)] [■8(𝑥@𝑦@𝑧)] = 𝟏/𝟔 [■8(2(3)+2(17)−4(7)@−4(3)+2(17)−4(7)@2(3)−1(17)+5(7))] [■8(𝑥@𝑦@𝑧)] = 𝟏/𝟔 [■8(12@−6@24)] [■8(𝑥@𝑦@𝑧)] = [■8(2@−1@4)] Hence x = 2 , y = −1 & z = 4

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.