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Find the inverse of the matrix [-3 2 5 -3] . Hence,  find the matrix P satisfying the matrix equation P [-3 2 5 -3] = [1 2 2 -1] .

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/


Find inverse of matrix [-3 2 5 -3]. Hence, find matrix P satisfying

Question 6 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2
Question 6 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3 Question 6 - CBSE Class 12 Sample Paper for 2018 Boards - Part 4

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Transcript

Question 6 Find the inverse of the matrix [■8(−3&[email protected]&−3)]. Hence, find the matrix P satisfying the matrix equation P [■8(−3&[email protected]&−3)] = [■8(1&[email protected]&−1)]. Let A = [■8(−3&[email protected]&−3)] We know that A-1 = 1/(|A|) adj A exists when |A|≠ 0 |A| = |■8(−3&[email protected]&−3)| = (–3) × (–3) – 5 × 2 = 9 – 10 = –1 Since |A|≠ 0, A–1 exists Calculating adj A A =[■8(−3&[email protected]&−3)] adj(A) = [■8(−3&[email protected]&−3)] = [■8(−3&−[email protected]−5&−3)] Calculating A–1 A-1 = 1/(|A|) adj A = 𝟏/(−𝟏) [■8(−3&−[email protected]−5&−3)] = −1[■8(−3&−[email protected]−5&−3)] = [■8(−1 × −3&−1 × −[email protected]−1 × −5&−1 × −3)] = [■8(𝟑&𝟐@𝟓&𝟑)] Now, P [■8(−3&[email protected]&−3)] = [■8(1&[email protected]&−1)] PA = [■8(1&[email protected]&−1)] P = [■8(1&[email protected]&−1)]A–1 Putting value of A–1 P = [■8(1&[email protected]&−1)][■8(3&[email protected]&3)] P = [■8(1(3)+2(5)&1(2)+2(3)@2(3)+(−1)5&2(2)+(−1)3)] P = [■8(3+10&[email protected]−5&4−3)] P = [■8(𝟏𝟑&𝟖@𝟏&𝟏)]

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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.