- #1
albaboi123
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i'm studying for my midterm and I'm stumped on this section about Lienar Transformations...hope u guys can help
question goes something like this
1) Find the standard matrix for the linear operator define by the equations (which is easy)
and then determine wheter the operator is one-to-one and or onto
example question is
w1=-x+3y+2z
w2=2x+4z
w3=x+3y+6z
2) Show that the range of the linear operator defined by the equations
w1=4x-2y
w2=2x-y
is not all of R^2, and find a vector that's not in the range.
1) so the standard matrix is
[-1 3 2]
[2 0 4]
[1 3 6]
now how do i tell if its 1-1 and/or onto?
Homework Statement
question goes something like this
1) Find the standard matrix for the linear operator define by the equations (which is easy)
and then determine wheter the operator is one-to-one and or onto
example question is
w1=-x+3y+2z
w2=2x+4z
w3=x+3y+6z
2) Show that the range of the linear operator defined by the equations
w1=4x-2y
w2=2x-y
is not all of R^2, and find a vector that's not in the range.
The Attempt at a Solution
1) so the standard matrix is
[-1 3 2]
[2 0 4]
[1 3 6]
now how do i tell if its 1-1 and/or onto?