Solution Found!
[M] Let b = and let A be the matrix in Exercise.Is b in
Chapter 1, Problem 40E(choose chapter or problem)
[M] Let \(\mathbf{b}=\left[\begin{array}{r}-7 \\ -7 \\ 13 \\ -5\end{array}\right]\) and let A be the matrix in Exercise. Is b in the range of the transformation \(\mathbf{x} \mapsto A \mathbf{x}\)? If so, find an x whose image under the transformation is b.
Questions & Answers
QUESTION:
[M] Let \(\mathbf{b}=\left[\begin{array}{r}-7 \\ -7 \\ 13 \\ -5\end{array}\right]\) and let A be the matrix in Exercise. Is b in the range of the transformation \(\mathbf{x} \mapsto A \mathbf{x}\)? If so, find an x whose image under the transformation is b.
ANSWER:Solution
Step 1
In this problem we need to determine whether b is in the range of the transformationor not. If so we have to find the vector x whose image under T is b.
Given: image of x under T is b. That is
Hence
To determine: is consistent or not.
We have
Put the corresponding values in