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Which one of the following matrices is diagonalisable, working over R? -1 0 1 0 4 0 0 0 -1 O 2 0 1 0 -1 0 -1 0 4 1 1 0 0 1 0

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Answer #1

ANSWER : OPTION (E)

As We know that, matrix is An dizable if the sum diagonalizabl ai is equal to s dimensions the eigenspace checking option (asolve the equation (4-1) (-1-1) = 0 The Roots are: = -1 ne= -1 These are eigenvalues. 13=4 steps. Find the Find the corresponoptions (b) Checking - 2 let B = 0 -1 4. stepla Finding eigenvalues. IB-XIl=0 | 2-1 0 1 0 - 1-X = 0 -1 0 4-X + (27) (-4-1) (4step2. Find the corresponding eigenspaces Ej? 3 0 5 - 0 Perform Row operation : 10 E = o 0 0 E = span 0 1 who - 4 o 0 1 -1 Pe. checking option (c) let C = o o 3 stepl. Gegenvalue: Ic-xIlzo 1-1 I =0 1-) 0 3-71 (1-12(3-1)=0 15!,!, 3 corresponding EigenF3 = - o o o Eză span (18) two eigenvectors. Not Diagonalizable. have Here also we ANSWER: checking options I 0 let D = 31 Stcherking option (E) 2 let = co 0 2 - Step! Finding eigenvalues: 1-3 o 2-X 0 -1- =0 o 2 =0 4 + 4 A (1-1) (1-4) (-1-1) + (2-0)Perform Row operations: 0 -1 - Ez= 0 - 0 Ez a span (:] E 2 02 UJ 어 2 2 Perform Row operation こ E, o o 0 0 El = span or span (

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