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Misc 8 - Show that A2 - 5A + 7I = O, if A = [3 1 -1 2] - Miscellaneous

Misc. 8 - Chapter 3 Class 12 Matrices - Part 2

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Misc. 8 If A = [ 8(3&[email protected] 1&2)] , show that A2 5A + 7I = O First calculating A2 A2 = A.A A2 = [ 8(3&[email protected] 1&2)] [ 8(3&[email protected] 1&2)] = [ 8(3(3)+1( 1)&3(1)+1(2)@ 1(3)+2( 1)& 1(1)+2(2))] = [ 8(9 1&[email protected] 3 2& 1+4)] = [ 8(8&[email protected] 5&3)] A2 = [ 8(8&[email protected] 5&3)] Now calculating A2 5A 7I = [ 8(8&[email protected] 5&3)] 5 [ 8(3&[email protected] 1&2)] + 7 [ 8(1&[email protected]&1)] = [ 8(8&[email protected] 5&3)] [ 8(5(3)&5(1)@5( 1)&5(2))] + [ 8(7(1)&7(0)@7(0)&7(1))] = [ 8(8&[email protected] 5&3)] [ 8(15&[email protected] 5&10)] + [ 8(7&[email protected]&7)] = [ 8(8 15+7&5 [email protected] 5 ( 5)&3 10+7)] = [ 8(0&[email protected]&0)] = O = R.H.S. L.H.S = R.H.S Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.