a) A is invertible
b)A is row equivalent to I
c) A has n pivot positions
d)Ax = 0 has only the trivial solution
e)Columns of A are linearly independent
f) Linear transformations x |--> A x is 1-1
g) Ax = b has a solution for each b in F^n
h)Columns of A span F^n
i) Linear transformation x |--> A x is onto
j)there is an nxn matrix C such that CA=I
k)there is an nxn matrix D such that AD=I
l) A^T is invertible
Originally posted by AbnormalButSane
a) A is invertible
b)A is row equivalent to I
c) A has n pivot positions
d)A[b]x = 0 has only the trivial solution
e)Columns of A are linearly independent
f) Linear transformations x |--> A x is 1-1
g) Ax = b has a solution for each b in F^n
h)Columns of A span F^n
i) Linear transformation x |--> A x is onto
j)there is an nxn matrix C such that CA=I
k)there is an nxn matrix D such that AD=I
l) A^T is invertible [/B]
I need to memorize 8 or 10 of these.
nowplaying Foxie Lady by the JHE