Dillon is designing a card game where different colored cards are assigned point values. kryshna is trying to find the
value of each colored card. dillon gives him the following hints. if i have 3 green cards, 1 yellow card, and 2 blue cards
in my hand, my total is 9. if i discard 1 blue card, my total changes to 7. if i have 1 card of each color (green, yellow, and
blue), my cards total 1.
a. write a system of equations for each hand of cards if x is the value of green cards, y is the value of yellow
cards, and z is the value of blue cards.
b. solve the system using any method you choose.
c. let x =
xyz
and b =
971
find a matrix l so that the linear transformation equation ll= b would produce
image coordinates that are the same as the solution to the system of equations.
d. enter matrix l into a software program or app, and try to calculate its inverse. does l have an inverse? if so,
what is it?
e. calculate l−1
971
verify that the result is equivalent to the solution to the system you calculated in part (b).
why should the solutions be equivalent?