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Exercise 2.4.3

Avg difficulty 3.0

Decide whether

v=[444]\mathbf{v}=\left[\begin{array}{r}4\\ 4\\ 4\end{array}\right]

is a linear combination of the vectors

u1=[31−1],u2=[80−1]andu3=[2−21].\mathbf{u}_{1}=\left[\begin{array}{r}3\\ 1\\ -1\end{array}\right],\quad\mathbf{u}_{2}=\left[\begin{array}{r}8\\ 0\\ -1\end{array}\right]\quad\text{and}\quad\mathbf{u}_{3}=\left[\begin{array}{r}2\\ -2\\ 1\end{array}\right].

If yes, find the coefficients.

Selinger, Matrix Theory and Linear Algebra, Vectors in Rn, Linear combinations, Exercise 2.4.3

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.