Kernel and Range: Understanding Linear Transformation in Algebra

[matqkks]

Why are we interested in looking at the kernel and range (image) of a linear transformation on a linear algebra course?

 

[HallsofIvy]

If we are at all interested in a linear transformation, wouldn't we want to know all we could about it? Do you remember, in basic algebra, solving equations a lot? Same thing here. Finding the kernel of a linear transformation, A, is the same as findig all solutions to Ax= 0. Finding the image is the same as finding all b such that Ax= b has a solution.

 

[Sankaku]

HallsofIvy has made the vital point clear. For the OP, I just want to mention that the concepts of kernel and range are vitally important to all of linear algebra and (later) abstract algebra. They may seem unintuitive at first, but it is worth the effort...