1.7 stuff

Question 1

a vector is ____ if all its coordinates are 0. it is the zero vector

Answer 1

trivial

Question 2

a system of linear equations is _____ if the right side is the zero vector

Answer 2

homogenous

Question 3

vectors are _____ if the vector equation = 0

Answer 3

independent

Question 4

vectors are _____ if it only has the trivial solution

Answer 4

independent

Question 5

______ solutions are non-zero solutins

Answer 5

non trivial

Question 6

if a vector has a non-trivial solution then the vector is _______

Answer 6

dependent

Question 7

the columns of a matrix can only be independent if the ______ has only the trivial solution

Answer 7

ax= 0

Question 8

a set containing only one vector is always independent if it does not

Answer 8

= 0

Question 9

if a set containing only one vector =0, then it

Answer 9

would have many non-trivial solutions

Question 10

a set of 2 vectors is independent if they are _______ of each other

Answer 10

not multiples

Question 11

geometrically, a set of 2 vectors is ____ if they are on the same line and go through the origin

Answer 11

dependent

Question 12

if there are more columns than rows it is

Answer 12

dependent

Question 13

if a set contains the zero vector than it is

Answer 13

dependent

Question 14

An indexed set of vectors{v1……vp} in Rn is said to be _______
if the vector equation
x1v1 + x2v2 + .. xpvp = 0
has only the trivial solution.

Answer 14

linearly independent

Question 15

A \_\_\_\_\_\_ (or function or mapping) T from Rn to Rm is a rule that assigns
to each vector x inRn a vector T .x/ inRm.

Answer 15

transformation