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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Question: Determine whether the statements that follow are true or false, and justify your answer.
19. There exits a matrix A such that.
If Ais an \(n \times n\) matrix and the transformation \({\bf{x}}| \to A{\bf{x}}\) is one-to-one, what else can you say about this transformation? Justify your answer.
In Exercise 2, compute \(u + v\) and \(u - 2v\).
2. \(u = \left[ {\begin{array}{*{20}{c}}3\\2\end{array}} \right]\), \(v = \left[ {\begin{array}{*{20}{c}}2\\{ - 1}\end{array}} \right]\).
Let \({{\mathop{\rm a}\nolimits} _1} = \left[ {\begin{array}{*{20}{c}}1\\4\\{ - 2}\end{array}} \right],{{\mathop{\rm a}\nolimits} _2} = \left[ {\begin{array}{*{20}{c}}{ - 2}\\{ - 3}\\7\end{array}} \right],\) and \({\rm{b = }}\left[ {\begin{array}{*{20}{c}}4\\1\\h\end{array}} \right]\). For what values(s) of \(h\) is \({\mathop{\rm b}\nolimits} \) in the plane spanned by \({{\mathop{\rm a}\nolimits} _1}\) and \({{\mathop{\rm a}\nolimits} _2}\)?
In Exercises 6, write a system of equations that is equivalent to the given vector equation.
6. \({x_1}\left[ {\begin{array}{*{20}{c}}{ - 2}\\3\end{array}} \right] + {x_2}\left[ {\begin{array}{*{20}{c}}8\\5\end{array}} \right] + {x_3}\left[ {\begin{array}{*{20}{c}}1\\{ - 6}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0\\0\end{array}} \right]\)
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