In this problem, allow T_1: mathbb{R}^2 rightarrow mathbb{R}^2 and T_2: mathbb{R}^2 rightarrow mathbb{R}^2 be linear transformations. Find Ker(T_1), Ker(T_2), Ker(T_3) of the respective matrices:A=begin{bmatrix}1 & -1 -2 & 0 end{bmatrix} , B=begin{bmatrix}1 & 5 -2 & 0 end{bmatrix}

Bergen

Bergen

Answered question

2020-10-20

In this problem, allow T1:R2R2 and T2:R2R2 be linear transformations. Find Ker(T1),Ker(T2),Ker(T3) of the respective matrices:
A=[1120],B=[1520]

Answer & Explanation

rogreenhoxa8

rogreenhoxa8

Skilled2020-10-21Added 109 answers

Step 1
T1:R2R2 and T2:R2R2
A=[1120],B=[1520] are matrices with respect to T1 and T2 Then if xKer(T1) Then T1(x)=0 i.e. Ax=0[1120][x1x2]=[00]
x1x2=0,2x1=0x1=0
x1=x2x2=0
So x=(00) only so Ker(T1)={(00)}
Let xKer(T2)T2(x)=0 and Bx=0
[1520][x1x2]=[00]x1+5x2=0,2x1=0
x1=0 and x2=0
So x=(00)
i.e. Ker(T2)={(00)}
Answer is as above

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?