In Excrcises 9-18 mark each statcment True or Falsc (T/F). Justify cach answcr. 9. (T/F) If vi.... ,Vp are in R" and if the set {vi-V2, V3 – V2....,Vp-V2} is linearly dependent, then {v1.....Vp} is affinely dependent. (Read this carefully.) | in DA iben

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.2: Corresponding Parts Of Congruent Triangles
Problem 16E: Given: HJ bisects KHL HJKL In Exercise 15, you cam delete Step 5 and 6 and still prove that KL. What...
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the baryccntric coord
nonnegative.
18. (T/F) If T is a triangle i
of the triangle, then the l
triangle) arc not all posi
In Excrcises 9-18 mark each statement True or Falsc (T/F). Justify
cach answcr.
9. (T/F) If v....,Vp are in R" and if the set {vi- V2, V3 –
V2....,Vp-V2} is linearly dependent, then {v...., Vp} is
affinely dependent. (Read this carefully.)
10. (T/F) If {v1....,Vp} is an aflinely dependent set in R", then
the set {V1..
linearly independent.
Vp) in R"+ of homogcncous forms may be
11. (T/F) If v.
forms (v1.....
{v.....Vp} is affinely dependent.
are in R" and if the set of homogeneous
ve} in R"+ is lincarly indepcndent, then
12. (T/F) If V1, V2, V3, and v4 are in R and if the set
{v2 - V1.V3- V1. V4 - V1} is linearly independent, then
{v....V4} is affincly independent.
13. (T/F) A finite set of points {v...., Vk} is affinely dependent
if there exist rcal numbers ci..
C1++ C = I and ci Vi +
Ck. not all zero, such that
..
...
Transcribed Image Text:the baryccntric coord nonnegative. 18. (T/F) If T is a triangle i of the triangle, then the l triangle) arc not all posi In Excrcises 9-18 mark each statement True or Falsc (T/F). Justify cach answcr. 9. (T/F) If v....,Vp are in R" and if the set {vi- V2, V3 – V2....,Vp-V2} is linearly dependent, then {v...., Vp} is affinely dependent. (Read this carefully.) 10. (T/F) If {v1....,Vp} is an aflinely dependent set in R", then the set {V1.. linearly independent. Vp) in R"+ of homogcncous forms may be 11. (T/F) If v. forms (v1..... {v.....Vp} is affinely dependent. are in R" and if the set of homogeneous ve} in R"+ is lincarly indepcndent, then 12. (T/F) If V1, V2, V3, and v4 are in R and if the set {v2 - V1.V3- V1. V4 - V1} is linearly independent, then {v....V4} is affincly independent. 13. (T/F) A finite set of points {v...., Vk} is affinely dependent if there exist rcal numbers ci.. C1++ C = I and ci Vi + Ck. not all zero, such that .. ...
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