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Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. Th...

Question

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form $(x, y),$ where $x \geq 0,$ with the standard operations on $R^{2}$

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form $(x, y),$ where $x \geq 0,$ with the standard operations on $R^{2}$



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Let $W$ be the set of all vectors of the form shown, where $a, b,$ and $c$ represent arbitrary real numbers. In each case, either find a set $S$ of vectors that spans $W$ or give an example to show that $W$ is not a vector space.
$\left[\begin{array}{l}{-a+1} \\ {a-6 b} \\ {2 b+a}\end{array}\right]$


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