Chapter 6.2, Problem 48E

Consider the linear transformation $T\left(\stackrel{\to }{x}\right)=\det \left[\begin{array}{ccccc}|& |& & |& |\\ {\stackrel{\to }{v}}_1& {\stackrel{\to }{v}}_2& \cdots & {\stackrel{\to }{v}}_{n-1}& \stackrel{\to }{x}\\ |& |& & |& |\end{array}\right]$ from ${ℝ}^n$ to ${ℝ}^n$ , where ${\stackrel{\to }{v}}_1,\mathrm{...},{\stackrel{\to }{v}}_{n-1}$ , are linearly independent vectors in ${ℝ}^n$ . Describe image and kernel ofthis transformation, and determine their dimensions.