[Solution Library] True or False. You must explain the reason for your answer. a: If u, v, w ∈ R^n and F is a linear transformation, then F(u); F(v);
Question: True or False. You must explain the reason for your answer.
a: If u, v, w \(\in {{\mathbb{R}}^{n}}\) and F is a linear transformation, then F(u); F(v); F(w) determine \(2u-3v+4w\).
a: If a 5 by 5 matrix A has rank 5; then any linear system of equations with coefficient matrix A will have a unique solution.
b: There exists a 2 \(\times \) 2 matrix B so that
\[B\left( \begin{matrix} 1 \\ 1 \\ \end{matrix} \right)=\left( \begin{matrix} 1 \\ 2 \\ \end{matrix} \right)\]and
\[B\left( \begin{matrix} 2 \\ 2 \\ \end{matrix} \right)=\left( \begin{matrix} 2 \\ 1 \\ \end{matrix} \right)\]c: Let A be a matrix of size 3 \(\times \) 5. Assume that the equation
\[Ax=\left( \begin{matrix} 1 \\ 2 \\ 4 \\ \end{matrix} \right)\]has a solution. Then it has infinitely many solutions.
Deliverable: Word Document 
