Given the basis β={(1,−1,3),(−3,4,9),(2,−2,4)}β={(1,−1,3),(−3,4,9),(2,−2,4)} and x=(8,−9,6)x=(8,−9,6), I am to find the corresponding coordinate vector [x]β[x]β. I claim that the coordinate vectors entries x1,x2,x3x1,x2,x3 meet the following criterion: x1(1,−1,3)+x2(−3,4,9)+x3(2,−2,4)=(8,−9,6)x1(1,−1,3)+x2(−3,4,9)+x3(2,−2,4)=(8,−9,6)This is equivalent to solving the augmented matrix ⎡⎣⎢1−13−3492−248−96⎤⎦⎥[1−328−14−2−93946]which is row equivalent to ⎡⎣⎢100−31020−18−10⎤⎦⎥
Step-by-step explanation: At the start of the equation, it said that on the blueprint every 4 feet in real life, there is one inch on the blueprint. If the width of the door if 4 feet in real life, than the width if the door on the blueprint is 1 inch.