Answer:
C. T is not one-to-one because the standard matrix A has a free variable.
Step-by-step explanation:
Given

Required
Determine if it is linear or onto
Represent the above as a matrix.
![T(x_1,x_2,x_3) = \left[\begin{array}{ccc}1&-5&4\\0&1&-6\\0&0&0\end{array}\right] \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right]](https://tex.z-dn.net/?f=T%28x_1%2Cx_2%2Cx_3%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-5%264%5C%5C0%261%26-6%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%26x_2%26x_3%5Cend%7Barray%7D%5Cright%5D)
From the above matrix, we observe that the matrix does not have a pivot in every column.
This means that the column are not linearly independent, & it has a free variable and as such T is not one-on-one
The equation for this is quite simple. Take note x is the amount of shirts sold and 5.25 is the cost for each one to which they add a 75 setup fee.
So the equation will be
75+(5.25x)=
It is 6 because 1000 would not be the appropiate answer
X+3y=7
x-3y=1
add them together
x+3y=7
<u>x-3y=1 +
</u>2x+0y=8
2x=8
divide 2
x=4
subsitute
x+3y=7
4+3y=7
subtract 4
3y=3
divid 3
y=1
x=4
y=1
answer is A
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