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**Fpr the matrix find a basis for hte kernel and image of [itex} T_{A} [/itex] and find the rank and nullity of [itex] T_{A} [/itex]**

T is a linear transformation

T is a linear transformation

[tex] \left(\begin{array}{cccc} 2&1&-1&3 \\ 1&0&3&1 \\ 1&1&-4&2 \end{array} \right) [/tex]

the kernel of T simply means to find the null space of A right?

so when i row reduce i get

[tex] \left(\begin{array}{cccc} 1&0&3&1 \\ 0&1&-7&0 \\ 0&0&0&0 \end{array} \right) [/tex]

so do i simply find a 3x1 line matrix X such taht AX = 0

The image means something to do iwth the solution... but there is no augmented form given here... is there??

the basis of A will be the rank T right? Is base A = 2?? So the rank of T = 2?

the dimensio of the kernel is T is nullity of T... but i need to find the basis for the kernel first