Answer to Question #45231 in Matrix | Tensor Analysis for Francis

Question

1) M = [ [-2,1,0], [-11,4,1],[-18,6,1]]
a) solve the equation M [ [x] , [y], [z] ] = 3 [ [x] , [y] , [z] ]
b) solve the equation M [ [x], [y], [z] ] = 4 [ [x] , [y], [z] ]

2) A matrix S has eigenvalues 2, -3 and 5 with corresponding eigenvectors v1 = [ [1] , [-3] , [-2] ] , v2 = [ [-2], [7], [5] ] and v3 = [ [0], [0], [1]] respectively.
a) write down the values of Sv1, Sv2 and Sv3.
b) evaluate S[ [0], [1], [0]]
d) hence or otherwise find matrix S