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by: Huy Tran

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5

# Linear Algebra: Final exam study guide MATH2076

Marketplace > University of Cincinnati > Mathematics (M) > MATH2076 > Linear Algebra Final exam study guide
Huy Tran
UC

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A study guide covering from chapter 4 to chapter 7.1. Some contents are - Vector space/ subspace - Linearly independent set, basis - Isomorphism - Coordinate system/ coordinate mapping - Row s...
COURSE
Linear Algebra
PROF.
TYPE
Study Guide
PAGES
5
WORDS
KARMA
50 ?

## Popular in Mathematics (M)

This 5 page Study Guide was uploaded by Huy Tran on Friday April 22, 2016. The Study Guide belongs to MATH2076 at University of Cincinnati taught by Magda Peligrad in Winter 2016. Since its upload, it has received 31 views. For similar materials see Linear Algebra in Mathematics (M) at University of Cincinnati.

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Date Created: 04/22/16
×   ⃗⃗1⃗⃗2⃗⃗⃗3⃗ } ????⃗3⃗ ????2⃗⃗ ????????????⃗1⃗⃗ ⃗3⃗⃗ = 1 1⃗⃗ +2 2⃗⃗⃗ ????1⃗⃗2⃗????⃗3⃗ } ⃗1⃗⃗2⃗⃗ } ⃗1⃗????⃗2⃗ } ???? = {???? ,???? ,…,???? } ⃗⃗⃗⃗ ???? ???? 1 2 ???? ???? = ???? 1 1 ???? ????2 2⋯+ ???? ???? ???? ????⃗⃗ ????1,????2,…,???? ???? ????⃗ ???? ????1 ???? [????]???? = [ ] ⋮ ???????? ???? ↦ ????[ ] ???? ↦ => ???? 3 −1 ????1= [6],????2= [0 ] 2 1 3 −1 ???? = {6 ] [0 ]} 2 1 ???? ⃗ = ????⃗ ???? (???? − ????????) 3. det(???? − ????????) = 0 ???? 1 3 −5 [0 2 4 ] ???? 0 0 7 ???? − ????????) = 0 1 − ???? 3 −5 ( 0 2 − ???? 4 ) = 0 0 0 7 − ???? ???? − ???????? 1 − ???? 2 − ???? 7 − ???? = 0 => ???? = 1,2,7 ????1,????2,…,???????? ????1,????2,…,???????? ????1,????2,…,???????? 10 0 0 0 1 0 0 [0 −4 0] [−2 0 ] [0 −5 0 0] 0 0 5 0 4 0 0 −7 0 0 0 0 6 ????1,????2,…,???????? ???? ,???? ,…,???? ???? ???? ???? ???? × ⃗ ???????????? ???? ⃗ ,????) | ⃗ − ???? | ???? ⊥ ???? ???? ???? ⊥ ⊥ ⊥ ???? (???????????? ???? ) = ???????????? ???? (???????????? ????) = ???????????? ????  ????.???? = ????  ????−???? = ???? ???? ???? = ????̂ + ???? ????̂ ???? ⃗ ) ̂ = ????1 1⃗⃗ +2 2⃗⃗ + ⋯+ ???? ????⃗⃗ ????.⃗⃗???? ????????= 2 | ⃗????⃗ | ???? = ???? − ????̂ ????     6 −2 −1 [−2 6 −1] −1 −1 5 −1 −1 1 ???? = 8,⃗1⃗⃗ =1[]; ???? = 6,⃗2⃗⃗ −1[]; ???? = 3,⃗3⃗ = 1 ] 0 2 1 ????1⃗⃗2⃗ ????????⃗3⃗ 1 1 1 − − 2 √6 √3 √ 1 1 ⃗1⃗ = 1 ; ⃗2⃗⃗ =− √6 ; ⃗3⃗⃗ =√3 √ 2 [ ] 2 1 0 [ √6 ] [√3] − 1 − 1 1 8 0 0 √2 √6 √3 1 1 1 ???? = [0 6 0 ] ???? = √2 − √6 √3 0 0 3 2 1 [ 0 √6 √3] ???? × ????

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