Question Number 210155 by Spillover last updated on 01/Aug/24
Answered by A5T last updated on 01/Aug/24
Commented by A5T last updated on 01/Aug/24
$${C}\:{is}\:{the}\:{origin}\:{and}\:{redundant} \\ $$$${A}+{D}={C}\Rightarrow\:{A}\:{and}\:{D}\:{are}\:{linearly}\:{dependent} \\ $$$${E}−{F}={C}\Rightarrow\:{E}\:{and}\:{F}\:{are}\:{linearly}\:{dependent} \\ $$$${B}+{G}={C}\Rightarrow\:{B}\:{and}\:{G}\:{are}\:{linearly}\:{dependent} \\ $$$$\Rightarrow\:{Only}\:{three}\:{vectors}\:{are}\:{pairwise}\:{linearly} \\ $$$${independent}.\: \\ $$$${Hence},\:{the}\:{space}\:{is}\:\mathrm{3}-{dimensional}. \\ $$
Commented by Spillover last updated on 01/Aug/24
$${great} \\ $$