- #1
BitterX
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Homework Statement
let [itex]T:R^3 \rightarrow R^3[/itex]
be a Linear map,
and let [itex]B=\left \{ (1,1,1),(1,1,0),(1,0,1) \right \}[/itex]
be a Basis
and [itex](1,0,0)\in kerT[/itex][itex][T]_B=\begin{pmatrix}
a & 0 & b\\
3 & 2a & 1\\
2c& b & a
\end{pmatrix}[/itex]
a. find a,b,c
b. find a Basis for ImT
Homework Equations
The Attempt at a Solution
as for a.
I think that what we need to do is find a general vector (x,y,z)
and express (1,0,0) thorugh it
if we multiply the matrix by what we got we will have to get (0,0,0) (because (1,0,0) is in the kernel)
but I'm not sure how to express (1,0,0).
I think the vector (1,0,0) in the basis B is -1(1,1,1)+1(1,1,0)+1(1,0,1) and so is
(-x+y+z,0,0)
and for the matrix we have
-a+0+b=0
-3+2a+1=0
-2c+b+a=0
from the second equation:
a= 1
from the first
b=1
from the third
c=1
Am I right?
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