9. Linear Transformations

Kernel And Image — Quiz

Test your understanding of kernel and image with 5 practice questions.

Practice Questions

Question 1

What is the kernel of a linear transformation $T:V\to W$?

Question 2

For $T(x,y)=(x+y,x-y)$, what is $\ker(T)$?

Question 3

For $T(x,y)=(x,0)$, what is $\operatorname{Im}(T)$?

Question 4

If $T(x,y)=(2x,2y)$, what is the image of $T$?

Question 5

If $\dim(V)=5$ and $\dim(\operatorname{Im}(T))=3$, what is $\dim(\ker(T))$?