[M] Let b = and let A be the matrix in Exercise.Is b in

Chapter 1, Problem 40E

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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.

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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

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