+0  
 
0
71
3
avatar

If the \(2 \times 2\) matrix \(\mathbf{A}\) has an inverse and \((\mathbf{A} - 2 \mathbf{I})(\mathbf{A} - 4 \mathbf{I}) = \mathbf{0},\) then find \[\mathbf{A} + 8 \mathbf{A}^{-1}.\]

 Feb 21, 2022
 #1
avatar+32964 
+2

Like so:

 

 Feb 22, 2022
 #2
avatar
+2

Alternatively,

\(\displaystyle (A-2I)(A-4I)=A^{2}-6A+8I=0,\\ A^{2}+8I=6A,\\ A+8A^{-1}=6I.\)

 Feb 23, 2022
 #3
avatar+117224 
0

Thanks Alan and guest.

 

I always need reminding about matrices :)

 Mar 8, 2022

8 Online Users

avatar