T(v) = av represents the linear transformation t. find a basis for the kernel of t and the range of t.
a = [2 1]
[3 4]

Ker(T) has basis

Range(T) has basis

Step-by-step explanation:

If the matrix you wanted to represent  is , then:

.

So, to find ker(T) you must solve the homogenous equation

Using Gauss elimination we obtain the simpler equivalent system

Then, we have that

.

We have that . On this case we say that the basis is the empty set .

The range of is the set of vectors of the form

So,

Where the angle brakets denotes the span.

can you put the picture up?

step-by-step explanation: