Most Important Selected Qs for JEE AdvancedMathematicsMatrices
Given A= [ array ccc 2 & 0 & - 5 & & 0 0 & & 3 array ] For R- a, b , A⁻¹ exists and A⁻¹=A^2-5 b A+c l , when =1 . The value of a+5 b+c is :
Correct answer
17
Step-by-step solution
A= | array ccc 2 & 0 & - 5 & & 0 0 & & 3 array | ;|A|= | array ccc 2 & 0 & - 5 & & 0 0 & & 3 array | 0 aligned & 6 -5 ^2 =0 & (6-5 ) 0 & =0,6 / 5 aligned R- 0,6 / 5 A= | array ccc 2 & 0 & -1 5 & 1 & 0 0 & 1 & 3 array | |A|=6-5=1 ; Adj A= | array ccc 3 & -1 & 1 -15 & 6 & -5 5 & -2 & 2 array | A⁻¹= | array ccc 3 & -1 & 1 -15 & 6 & 5 5 & -2 & 2 array | By characteristic equation |A-x I|=0 aligned & | array ccc 2-x & 0 & -1 5 & 1-x & 0 0 & 1 & 3-x array |=0 & x^3-6 x^2+11 x-1=0 aligned By cayley hamilton theorem A^3-6