The vectors v1 leftvphantombeginarraycstrutstrutstrutstruten

The vectors v_1= \\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\ ight[ 3 \\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\ ight] -2 0 , v_2= \\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\ ight[ -5 \\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\ ight] 6 6 , and v_3= \\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\ ight[ -7 \\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\ ight] 10 k form a basis for {\\mathbb R}^3 if and only if k\ e

Solution