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Exercise 5

Avg difficulty 3.0

Find the system of equations resulting from starting with

h1,1x1+h1,2x2+h1,3x3=d1h2,1x1+h2,2x2+h2,3x3=d2\begin{array}{rcrcrcr}h_{1,1}x_{1}&+&h_{1,2}x_{2}&+&h_{1,3}x_{3}&=&d_{1}\\ h_{2,1}x_{1}&+&h_{2,2}x_{2}&+&h_{2,3}x_{3}&=&d_{2}\end{array}

and making this change of variable (i.e., substitution).

x1=g1,1y1+g1,2y2x2=g2,1y1+g2,2y2x3=g3,1y1+g3,2y2\begin{array}{rcrcr}x_{1}&=&g_{1,1}y_{1}&+&g_{1,2}y_{2}\\ x_{2}&=&g_{2,1}y_{1}&+&g_{2,2}y_{2}\\ x_{3}&=&g_{3,1}y_{1}&+&g_{3,2}y_{2}\end{array}

Hefferon, Linear Algebra, Maps Between Spaces, Matrix Multiplication, Exercise 5

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.