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

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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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&0@0&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&0@0&7)] = [ 8(8 15+7&5 5+0@ 5 ( 5)&3 10+7)] = [ 8(0&0@0&0)] = O = R.H.S. L.H.S = R.H.S Hence proved

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