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18 Nov 2019
Show that if AB=BA, then
v) (A+B)n = sum from k=0 to n (n choose k) Ak Bn-k
vi) etA etB = et(A+B)
vii) Show that if (A+B)2 = A2 + 2AB + B2, then AB=BA.
viii) Show that if etA etB = et(A+B) for all t>0, then AB=BA (Hint consider the coefficients of t2).
ix) Find etA if A = [3 1 0; 0 3 1; 0 0 3]
Show that if AB=BA, then
v) (A+B)n = sum from k=0 to n (n choose k) Ak Bn-k
vi) etA etB = et(A+B)
vii) Show that if (A+B)2 = A2 + 2AB + B2, then AB=BA.
viii) Show that if etA etB = et(A+B) for all t>0, then AB=BA (Hint consider the coefficients of t2).
ix) Find etA if A = [3 1 0; 0 3 1; 0 0 3]
akhilgoudLv3
15 Mar 2023
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Sixta KovacekLv2
6 Mar 2019
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