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?
+129845 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!!!
