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
Answer:
Step-by-step explanation:
3x - 2(x + 3) = 4x - 9 - x
Start by multiplying 2 by the values in the parenthesis
3x - 2x + 6 = 4x - 9 - x
Subtract 3x - 2x and 4x - x
x + 5 = 3x - 9
Add 9 to both sides of the equation
x + 14 = 3x
Subtract x from both sides of the equation
14 = 2x
Divide both sides of the equation by 2
Hope this helps :)
Answer:
B. Stratified random sample is the correct answer
Answer:
D
Step-by-step explanation:
