We can consider each unique
as the as the
-th unit vector. So your set
can be considered as the vectors
Then check for independence your favorite way. In this case, I'll see if the linear map A of the new basis vectors doesn't map to a subspace via the determinant not being zero:
![det(A) = det \left ( \left [ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 3 \\ 0 & 1 & 4 \end{array}\right ] \right ) = 1(4-3) = 1](https://tex.z-dn.net/?f=%20det%28A%29%20%3D%20det%20%5Cleft%20%28%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bccc%7D%201%20%26%200%20%26%200%20%5C%5C%200%20%26%201%20%26%203%20%5C%5C%200%20%26%201%20%26%204%20%5Cend%7Barray%7D%5Cright%20%5D%20%5Cright%20%29%20%3D%201%284-3%29%20%3D%201)
So they are linear independent.
Answer:How to simplify expressions with exponents and logs. • How to solve equations with ... 15) The temperature, T, of a given cup of hot chocolate after it has been cooling for tminutes can best be modeled by the function ...
Step-by-step explanation:How to simplify expressions with exponents and logs. • How to solve equations with ... 15) The temperature, T, of a given cup of hot chocolate after it has been cooling for tminutes can best be modeled by the function ...
Answer:
x=6.5
Step-by-step explanation:
Given the equation as
7(x-2)=3(x+4)
7x-14=3x+12--------------------------opening the brackets
7x-3x=12+14--------------------------collecting like terms
4x=26-----------------------------------solve for x by dividing both sides by 4
4x/4=26/4
x=6.5
The slope is 4/3.
rise/run
rise = 4
run = 3
Answer:
The answer is below
Step-by-step explanation:
The domain of a function is the set of all independent variables for the function while the range of a function is the set of all possible dependent variables.
Let x represent the number of newspaper lines and f(x) be the charges for advertisement. x is the independent variable and f(x) is the dependent variable.
Since the newspaper charges $3 per line for the first 4 lines plus a $20 fee to advertise, the function is given as:
f(x) = 3x + 20 for 0 < x < 4
But for more than four lines, the charges is given as:
f(x) = 12 + 20 = 32 4 < x < ∞
Therefore, the domain and range of the function is:
Domain = (0, ∞)
Range = (20, 32}
