{"version":8,"graph":{"viewport":{"xmin":-1.1591770373130892,"ymin":-0.9026117446145827,"xmax":8.559740786153274,"ymax":5.831855702744378}},"randomSeed":"1aae7678515b13a40bbd8386dda9febf","expressions":{"list":[{"type":"text","id":"46","text":"Taught/inspired by 3B1B EOLA CH13 https://www.youtube.com/watch?v=P2LTAUO1TdA"},{"type":"text","id":"37","text":"Jennifer's basis vectors"},{"type":"expression","id":"1","color":"#c74440","latex":"b_{1}=\\left[2,1\\right]","hidden":true,"lines":false},{"type":"expression","id":"38","color":"#6042a6","latex":"b_{2}=\\left[-1,1\\right]"},{"type":"text","id":"40","text":"Vector in our basis to translate"},{"type":"expression","id":"41","color":"#c74440","latex":"a=\\left[3,2\\right]"},{"type":"text","id":"43","text":"Translation (change of basis)"},{"type":"expression","id":"47","color":"#000000","latex":"c\\left[1\\right]b_{1}+c\\left[2\\right]b_{2}=a"},{"type":"expression","id":"49","color":"#2d70b3","latex":"xb_{1}+yb_{2}=a"},{"type":"expression","id":"50","color":"#388c46","latex":"xb_{1}=a-yb_{2}"},{"type":"expression","id":"51","color":"#6042a6","latex":"x=\\frac{a-yb_{2}}{b_{1}}"},{"type":"expression","id":"52","color":"#000000","latex":"y=\\frac{a-xb_{1}}{b_{2}}"},{"type":"text","id":"54","text":"Desmos is being weird (and/or I'm making mistakes)"},{"type":"text","id":"56","text":"But the intersection of the lines graphed is how the vector would be represented in Jennifer's basis"}]}}