Let \( S \) be the set of all column matrices \( \left[\begin{array}{l}b_{1} \\ b_{2} \\ b_{3}\e...

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Let \( S \) be the set of all column matrices \( \left[\begin{array}{l}b_{1} \\ b_{2} \\ b_{3}\end{array}\right] \) such that \( b_{1} \), \( b_{2}, b_{2} \in R \) and the system of equations (in real variables)
math xmlns=http://www.w3.org/1998/Math/MathML class=wrs_chemistrymtable columnalign=leftmtrmtdmo-/momix/mimo+/momn2/mnmiy/mimo+/momn5/mnmiz/mimo=/momsubmib/mimn1/mn/msub/mtd/mtrmtrmtdmn2/mnmix/mimo-/momn4/mnmiy/mimo+/momn3/mnmiz/mimo=/momsubmib/mimn2/mn/msub/mtd/mtrmtrmtdmix/mimo-/momn2/mnmiy/mimo+/momn2/mnmiz/mimo=/momsubmib/mimn3/mn/msub/mtd/mtr/mtable/math
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each \( \left[\begin{array}{l}b_{1} \\ b_{2} \\ b_{3}\end{array}\right] \in S ? \)
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