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## Homework Statement

For the linear transformation T: R4 --> R3 defined by T

_{A}: v -->Av

find a basis for the Kernel of T

_{A}and for the Image of of T

_{A}where A is

2 4 6 2

1 3 -4 1

4 10 -2 4

## Homework Equations

Let v =

a1 b1 c1

a2 b2 c2

a3 b3 c3

a4 b4 c4

## The Attempt at a Solution

so v is a 4x3 matrix, and Ker(T) would just be the solution for Av = 0.

I was unsure as to what the Image would be give by. Is it the matrix

2a1+4b1+6c1+2d1, 2a2+4b2+6c2+2d2, 2a3+4b3+6c3+2d3,

1a1+3b1-4c1+d1, ... etc

(just the general solution of the multiplication)

Which generalizes to

2 0 2

0 1 2

so the basis is [1, 2, -1]

How would I find a basis for the Kernel?

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