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# a. Consider the n n matrix B = 0 1 0 1 . . . . . . 0 1 0 . Calculate B2, B3, . . . , Bn

ISBN: 9781429215213 438

## Solution for problem 8 Chapter 7.3

Linear Algebra: A Geometric Approach | 2nd Edition

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Linear Algebra: A Geometric Approach | 2nd Edition

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Problem 8

a. Consider the n n matrix B = 0 1 0 1 . . . . . . 0 1 0 . Calculate B2, B3, . . . , Bn. (Hint: Bn = O.) b. Let J be an n n Jordan block with eigenvalue . Show that etJ = et tet 1 2 t 2et 1 (n1)! tn1et et tet 1 (n2)! tn2et . . . . . . ... et tet et . (Hint: Write J = I + B, and use Exercise 2.1.15 to find J k.)

Step-by-Step Solution:
Step 1 of 3

*"1 ilrr*r[rywK 1\; /ll*stqiravdv ,*''Jrr%l ,ffi r.'*9x* C] d: rSSx dl t, *sit*{X Ue*-- (rex)dx f)\$s ros {l&}fu ' \$:,n+("rex)*infltu}d^ =}k.n'{,r"IJl,n =[[l-rorz {te,h}k,,r(lzrHx {r=.a:adtzx} .rJa*. l*,:inft2dhr -\$ Yr-rr*1!u, -*.\$rr*&f+,,ra}&, . *#,,t * .\$ *3 r#*r5*{.-,*...

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a. Consider the n n matrix B = 0 1 0 1 . . . . . . 0 1 0 . Calculate B2, B3, . . . , Bn

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