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Let A be a matrix and x be a non-zero vector such that

A x = 2 x.

Then we have that

A^7 x = a x

some value of a. What is a equal to?

 May 25, 2019

Best Answer 

 #1
avatar+5664 
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\(A x = 2x\\ A^7x = A^6(Ax) =\\ A^6 (2x) = \\ 2 A^5(Ax) = 4 A^5 x\\ \text{etc. See if you can finish}\)

.
 May 25, 2019
 #1
avatar+5664 
+1
Best Answer

\(A x = 2x\\ A^7x = A^6(Ax) =\\ A^6 (2x) = \\ 2 A^5(Ax) = 4 A^5 x\\ \text{etc. See if you can finish}\)

Rom May 25, 2019
 #2
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i got the wrong answer. Do you know what the correct one is?

Guest May 27, 2019

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