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Chapter 1: Q30E (page 1)
Give an example of an inconsistent underdetermined system of two equations in three unknowns.
One of the examples of an inconsistent underdetermined system of two equations in three unknowns is
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Find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.
29. \(\left[ {\begin{array}{*{20}{c}}0&{ - 2}&5\\1&4&{ - 7}\\3&{ - 1}&6\end{array}} \right]\), \(\left[ {\begin{array}{*{20}{c}}1&4&{ - 7}\\0&{ - 2}&5\\3&{ - 1}&6\end{array}} \right]\)
In Exercise 19 and 20, choose \(h\) and \(k\) such that the system has
a. no solution
b. unique solution
c. many solutions.
Give separate answers for each part.
19. \(\begin{array}{l}{x_1} + h{x_2} = 2\\4{x_1} + 8{x_2} = k\end{array}\)
Give a geometric description of Span \(\left\{ {{v_1},{v_2}} \right\}\) for the vectors in Exercise 16.
Determine the values(s) of \(h\) such that matrix is the augmented matrix of a consistent linear system.
18. \(\left[ {\begin{array}{*{20}{c}}1&{ - 3}&{ - 2}\\5&h&{ - 7}\end{array}} \right]\)
Determine whether the statements that follow are true or false, and justify your answer.
15: The systemisinconsistent for all matrices A.
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