Linear maps: Linear maps
Sums and multiples of linear maps
Consider the linear maps #F# and #G# from #\mathbb{R}^2# to #\mathbb{R}^2# given by
\[\begin{array}{rcl}F(\rv{x,y}) &=& \rv{-{\it x}-2 {\it y},3 {\it y}-5 {\it x}}\\
G(\rv{x,y}) &=& \rv{3 {\it x}-6 {\it y}, 3 {\it y}-3 {\it x}}\end{array}\]
Determine a vector #\rv{ax+by,cx+dy}# with real numbers #a#, #b#, #c#, and #d# that gives a function rule for
\[-8\cdot F -6\cdot G\]
\[\begin{array}{rcl}F(\rv{x,y}) &=& \rv{-{\it x}-2 {\it y},3 {\it y}-5 {\it x}}\\
G(\rv{x,y}) &=& \rv{3 {\it x}-6 {\it y}, 3 {\it y}-3 {\it x}}\end{array}\]
Determine a vector #\rv{ax+by,cx+dy}# with real numbers #a#, #b#, #c#, and #d# that gives a function rule for
\[-8\cdot F -6\cdot G\]
#(-8\cdot F -6\cdot G)(\rv{x,y})= # |
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