Ex 4.4, 14 - Chapter 4 Class 12 Determinants
Last updated at April 16, 2024 by Teachoo
Finding inverse when Equation of matrice given
Finding inverse when Equation of matrice given
Last updated at April 16, 2024 by Teachoo
Ex 4.4, 14 For the matrix A = [■8(3&2@1&1)] , find the numbers a and b such that A2 + aA + bI = O. Finding A2 A2 = A.A = [■8(3&2@1&1)] [■8(3&2@1&1)] = [■8(3(3)+2(1)&3(2)+2(1)@1(3)+1(1)&1(2)+1(1))] = [■8(9+2&6+2@3+1&2+1)] = [■8(11&8@4&3)] Now, A2 + aA + bI = O Putting values [■8(11&8@4&3)] + a [■8(3&2@1&1)] + b [■8(1&0@0&1)] = O [■8(11&8@4&3)] + [■8(3a&2a@a&a)] + [■8(b&0@0&b)] = O [■8(11+3a+b&8+2a+0@4+a+0&3+a+b)] = O [■8(3a+b+11&2a+8@4+a&a+b+3)] = [■8(0&0@0&0)] Since the matrices are equal, Comparing corresponding elements 3a + b + 11 = 0 2a + 8 = 0 4 + a = 0 a + b + 3 = 0 Solving (3) a + 4 = 0 a = –4 Putting value a in (1) 11 + 3 a + b = 0 11 + 3 (–4) + b = 0 11 – 12 +b = 0 –1 + b = 0 b = 1 Hence, a = −4, b = 1