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5 1 0 Problem 4: LetA = 0 41 . Consider the linear operator LA : R3 → R3 a) Find the characterist...

5 1 0 Problem 4: LetA = 0 41 . Consider the linear operator LA : R3 → R3 a) Find the characteristic polynomial for LA b) Let

5 1 0 Problem 4: LetA = 0 41 . Consider the linear operator LA : R3 → R3 a) Find the characteristic polynomial for LA b) Let V-Null(A 51). V is an invariant subspace for LA. Pick a basis B for V and c) Let W-Null(A 51)2). W is an invariant subspace for LA Pick a basis a for W 0 3 2 use it to find LAlvls and the characteristic polynomial of LAl and use it to find LAlwla and the characteristic polynomial of LAlw. d Let. Show that the cyclic subspace generated by v is 3-dimensional y be the ordered basis , Av, Av. What is the characteristic polynomial of [LAJ? e) Let
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5 4- (Lu3) (o4,2) [.uts hea] 432)chasactesic プ yCA-52) O-4. 43 o 33QVecto饥 the hmea tal of LAl4- 4- IG+12 -6-12 /2+9 12-0 o4 4 23-23 (X3.2) e R3 :-43442. 238-232,-28-212 6x,33 LA(k). 2A (χ.IJ)х. 2x2(4, 12, 16 (2. 76, 63) 3 (4,12,16)+olo.4,2) LAv) LA (12,76.63) ;凸LA (4,12,16)-16 LA Cong) 巴 Cucl2 Mastatfe vectousdinGO):3 IOlo od궁

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5 1 0 Problem 4: LetA = 0 41 . Consider the linear operator LA : R3 → R3 a) Find the characterist...
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