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Let A be a matrix and x be a non zero vector \(Ax=2x\). Then we have that  \(A^7x=mx\) for some value m. What is m equal to?

 Jul 8, 2019
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Ax =  2x

A * Ax   =  A * (2x)  = 2(Ax) = 2(2x)  = 4x = A2x

A * A2x  =  A* (4x)  =  4(Ax)  = 4(2x) = 8x  = A3x

A * A3x  =  A(8x)  = 8 (Ax)  = 8(2x) = 16x = A4x

A * A4x  =  A(16x)  = 16 (Ax)  = 16 (2x)  = 32x  = A5x

A * A5x  =  A (32x)  = 32(Ax)  = 32(2x) = 64x  = A6x

A * A6x  =  A(64x) = 64(Ax)  = 64 (2x) = 128x = A7x

 

 

So.....m  = 128

 

Correction.....thx, heureka!!!

 

 

cool cool cool

 Jul 8, 2019
edited by CPhill  Jul 9, 2019

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