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Misc 5 - Chapter 3 Class 12 Matrices

Last updated at May 29, 2023 by

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&1@ 1&2)] , show that A2 5A + 7I = O First calculating A2 A2 = A.A A2 = [ 8(3&1@ 1&2)] [ 8(3&1@ 1&2)] = [ 8(3(3)+1( 1)&3(1)+1(2)@ 1(3)+2( 1)& 1(1)+2(2))] = [ 8(9 1&3+2@ 3 2& 1+4)] = [ 8(8&5@ 5&3)] A2 = [ 8(8&5@ 5&3)] Now calculating A2 5A 7I = [ 8(8&5@ 5&3)] 5 [ 8(3&1@ 1&2)] + 7 [ 8(1&[email protected]&1)] = [ 8(8&5@ 5&3)] [ 8(5(3)&5(1)@5( 1)&5(2))] + [ 8(7(1)&7(0)@7(0)&7(1))] = [ 8(8&5@ 5&3)] [ 8(15&5@ 5&10)] + [ 8(7&[email protected]&7)] = [ 8(8 15+7&5 5+0@ 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.