Given Matrix transformation matrix \(A =\begin{pmatrix} 1 & 1

Kristina Mcclain

Kristina Mcclain

Answered question


Given Matrix transformation matrix
Are there vectors in R3 that do not change under this transformation, i.e. such that T(u)=u? Explain why yes or why not.

Answer & Explanation

Ronald Alvarez

Ronald Alvarez

Beginner2022-02-03Added 11 answers

Step 1
for any λ
A little work shows that these are the only solutions to
A note: no matter what linear transformation you have, T(0)=0 is always true, but sometimes students forget to state the whole problem, so I posted a complete set of solutions just in case
Gwendolyn Meyer

Gwendolyn Meyer

Beginner2022-02-04Added 11 answers

Step 1
Third equation gives z=0 and first equation gives y=0. So,
for any xR.

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