If A=[1&2 -1&3] and if A6=K A-205 I then

Question

If A=[1&2 -1&3] and if A6=K A-205 I then (A) K=11 (B) K=22 (C) K=33 (D) K=44

Tardigrade Admin · Accepted Answer

A=[1&2 -1&3] ⇒ A2 =[1&2 -1&3][1&2 -1&3]= [-1&8 -4&7] =4A -5I ⇒ A3 =A A2=A(4 A-5 I) =4 A2-5 A =4(4 A-5 I)-5 A =11 A-20 I A6 =A3 ⋅ A3=(11 A-20 I)2 =121 A2-440 A+400 I =121(4 A-5 I)-440 A+400 I =44 A-205 I

Q. If $A = [1 - 1 23]$ and if $A^{6} = K A - 205 I$ then

$K = 11$

$K = 22$

$K = 33$

$K = 44$

Q. If A=[1−1​23​] and if A6=KA−205I then

K=11

K=22

K=33

K=44

A=[1−1​23​] ⇒A2=[1−1​23​][1−1​23​]= [−1−4​87​] =4A−5I ⇒A3=AA2=A(4A−5I) =4A2−5A =4(4A−5I)−5A =11A−20I A6=A3⋅A3=(11A−20I)2 =121A2−440A+400I =121(4A−5I)−440A+400I =44A−205I

Q. If $A = [1 - 1 23]$ and if $A^{6} = K A - 205 I$ then

$K = 11$

$K = 22$

$K = 33$

$K = 44$