Chapter 11.2, Problem 57ES

A vector w is said to be a liner combination of the vectors ${\text{v}}_1$ and ${\text{v}}_2$ if w can be expressed as $\text{w}={\text{c}}_1{\text{v}}_1+{\text{c}}_2{\text{v}}_2,$ where $c_1\text{and}{c}_2$ are scalars.

(a) Find scalars ${\text{c}}_1$ and ${\text{c}}_2$ to express the vector 4j as a liner combination of the vector ${\text{v}}_1=2\text{i}-{\text{j and v}}_2=4\text{i}+2\text{j}.$

(b) Show that the vector $〈3,5〉$ cannot be expressed as a linear combination of the vector ${\text{v}}_1=〈1,-3〉{\text{v}}_2=〈-2,6〉.$