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⎤⎦⎥
Y=Mx+b
Slope/M= -1
X= 3
Y= -1
-1 = -1(3)+b
-1 = -3 + b
Add +3 to -3 and -1 to cancel -3 out to get (b)
-3+3 = 0 cancel it
-1 +3 = 2
So, b = 2
In an equation it will be written as
y= -1x + 2
In standard form it will be
1x + y = 2
But your official answer will be
B= 2
Y= -1x+2
The solution of the equation after solve the equation, 2x − 3 4x = 21 is 4. Option 3 is correct.
<h3>How to obtain the solution of equation?</h3>
To obtain the solution of an equation, the similar terms should be arranged together and then mathematical operation need to be performed to simplify it.
The equation which is provided to solve is,
To solve this equation, arrange the like terms as,
Add number 3 both side of the equation as,
Divide both side of the equation with number 6, we get,
Hence, the solution of the equation after solve the equation, 2x − 3 4x = 21 is 4. Option 3 is correct.
Learn more about the solution of the equation here;
brainly.com/question/21283540
Answer:
18 novels
Step-by-step explanation:
X= number of novels, 12.25 is a fixed fee.
9.50x+12.25=183.25
9.50x=171
x=18 novels