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

Question #45231

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

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

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