# Sets of Linear Combinations and Their Images under Linear Transformations

Sets of Linear Combinations and Their Images under Linear Transformations

This Demonstration visualizes points, vectors, and the effect of linear transformations from to . The black and red vectors are linear combinations of and given by and , respectively. The green dots are integral scalar multiples of , and , and the black dots show the images of the green dots under the linear transformation defined by the matrix .

3

R

3

R

a

b

3a+2b

2a-b+c

a,b

c

A