Question

Let A be a 3x3 matrix which has determinant 3 and satisfies the equation A^2-7A +4I= 0.Find the
value of |det(A-2I)|​

Answer 1

Answer:

A^2–7A+4I=0

A^2–4A+4(I*I)=3A [I*I=I]

A^2–2*A*2I+(2I)^2=3A

(A-2I)^2=3A

Det (A-2I)^2= Det (3A)

Det(A-2I)*Det(A-2I)= 27Det(A) [Det(cA) = c^n*Det(A), n= order of matrix.]

Det (A-2I)=(27*3)^0.5

Det (A-2I) = 9 [Det (A-2I) >=Det (A)+ Det (-2I) , Det (A-2I) >= Det (A)- 8 Det of (I), Det (A-2I) >=3–8,Det (A-2I) >=-5]

Det (A-2I) =9.

Step-by-step explanation:

Answer 2

Answer:3x3=9

Step-by-step explanation:Study hard