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⎤⎦⎥
13 times 3 equals 39. So 13 and 3 are the two numbers.
Answer:
26/15
Step-by-step explanation:
tadatada googoogaga
9514 1404 393
Answer:
Step-by-step explanation:
The ratio of the larger to the smaller corresponding sides is ...
12.5/5 = 2.5
That means ...
x = 2.5 × 4 = 10
y = 2.5 × 3 = 7.5