QuestionQuestion 1 [10 points]
Consider the following matrix:
For each of the following vectors, determine whether it is in the image and/or null space of . If the vector is in the image of find a vector so that .
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< Select an answer >
Studdy Solution
To find such that , solve the reduced system:
\begin{align*}
x_1 - x_2 + x_3 &= -2 \\
2x_2 + 2x_3 &= 3
\end{align*}
From the second equation, solve for :
Substitute into the first equation:
Thus, one solution is:
The results are:
- is not in the image of but is in the null space.
- is in the image of and a solution for is .
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