Check sibling questions

    Slide11.JPG

Slide12.JPG
Slide13.JPG Slide14.JPG Slide15.JPG Slide16.JPG

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


Transcript

Ex 4.5, 5 Examine the consistency of the system of equations. 3x − y − 2z = 2 2y − z = −1 3x − 5y = 3 The system of equations can be written as 3x − y − 2z = 2 0x + 2y − z = −1 3x − 5y + 0z = 3 Writing equation as AX = B [■8(3&−1&−2@0&2&−1@3&−5&0)] [■8(𝑥@𝑦@𝑧)] = [■8(2@1@3)] Hence A = [■8(3&−1&−2@0&2&−1@3&−5&0)], X = [■8(𝑥@𝑦@𝑧)] & B = [■8(2@1@3)] Calculating |A| |A| = |■8(3&−1&−2@0&2&−1@3&−5&0)| = 3 |■8(2&−1@−5&0)| – (–1) |■8(0&−1@3&0)| − 2 |■8(0&2@3&−5)| = 3(0 – 5) + 1 (0 + 3) –2 (0 – 6)= 3 (–5) + 1 (3) –2 (–6) = –15 + 3 + 12 = –15 + 15 = 0 Since |A| = 0, We calculate adj A (B) adj A = [■8(A_11&A_12&A_13@A_21&A_22&A_23@A_31&A_32&A_33 )]^′= [■8(A_11&A_21&A_31@A_12&A_22&A_32@A_13&A_32&A_33 )] A = [■8(3&−1&−2@0&2&−1@3&−5&0)] M11 = |■8(2&−1@−5&0)| = 0 – (5) = – 5 M12 = |■8(0&−1@3&0)| = 0 + 3 = –3 M13 = |■8(6&2@3&−5)| = 0 – 6 = – 6 M21 = |■8(−1&−2@−5&0)| = 0 – 10 = – 10 M22 = |■8(3&−2@3&0)| = 0 + 6 = 6 M23 = |■8(3&−1@3&−5)| = – 15 +3 = – 12 M31 = |■8(−1&−2@2&−1)| = 1 + 4 = 5 M32 = |■8(3&−2@0&−1)| = – 3 + 0 = – 3 M33 = |■8(3&−1@0&2)| = 6 + 0 = 6 Now, A11 = (–1)1+1 . M11 = (–1)2 . (–5) = –5 A12 = (–1)1+2 . M12 = (–1)3 . 3 = –3 A13 = (–1)1+3 . M13 = (–1)4 . (–6) = –6 A21 = (–1)2+1 . M21 = (–1)3 . (–10) = 10 A22 = (–1)2+2 . M22 = (–1)4 . 6 = 6 A23 = (–1)2+3 . M23 = (–1)5 . (–12) = 12 A31 = (–1)3+1 . M31 = (–1)4 . 5 = 5 A32 = (–1)3+2 . M32 = (–1)5 . (–3) = 3 A33 = (–1)3+3 . M33 = (–1)6 . (6) = 6 Thus, adj (A) = [■8(A_11&A_21&A_31@A_12&A_22&A_32@A_13&A_32&A_33 )] = [■8(3&−1&−2@0&2&−1@3&−5&0)] Now, adj (A) . B Putting values = [■8(−5&10&5@−3&6&3@−6&12&6)] [■8(2@−1@3)] = [■8(−5(2)+10(−1)+5(3)@−3(2)+6(−1)+3(3)@−6(2)+12(−1)+6(3) )] = [■8(−10−10+15@−6−6+9@−12−12+18)] = [■8(−5@−3@−6)] Thus, adj A . B ≠ O Since |A| = 0 & (adj A) B ≠ O, Thus, the given system equation is inconsistent & the system of equations has no solution

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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.