Question

Let T(V)=AV be a linear transformation where A=(3 -2 6 -1 15, 4 3 8 10...

Let T(V)=AV be a linear transformation where A=(3 -2 6 -1 15, 4 3 8 10 -14, 2 -3 4 -4 20)

a.) construct a basis of the kernal T

b.) calculate the basis of the range of T

c.) determine the rank and nullity of T

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Homework Answers

Answer #1
3 -2 6 -1 15
4 3 8 10 -14
2 -3 4 -4 20

Divide row1 by 3

1 -2/3 2 -1/3 5
4 3 8 10 -14
2 -3 4 -4 20


Add (-4 * row1) to row2

1 -2/3 2 -1/3 5
0 17/3 0 34/3 -34
2 -3 4 -4 20


Add (-2 * row1) to row3

1 -2/3 2 -1/3 5
0 17/3 0 34/3 -34
0 -5/3 0 -10/3 10


Divide row2 by 17/3

1 -2/3 2 -1/3 5
0 1 0 2 -6
0 -5/3 0 -10/3 10


Add (5/3 * row2) to row3

1 -2/3 2 -1/3 5
0 1 0 2 -6
0 0 0 0 0


Add (2/3 * row2) to row1

1 0 2 1 1
0 1 0 2 -6
0 0 0 0 0

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