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:
B)
Step-by-step explanation:
In statistics, an outlier is a data point that differs significantly from other observations.
This can happen because of different reasons: it may be due to variability in the measurement or it may indicate an actual experimental error. If it is an actual experimental error then it can create problems when doing the statistical analysis.
A) We can say that this is true, the outliers are observed values far from the other data, however we can make a much deeper analysis of this.
B) This is the right answer, since we don't know what is really causing the outlier, we need to take a closer look to see if they are just mistakes (and therefore be removed). If they are not mistakes we need to do the analysis with and without them to reach correct conclusions.
C) this is wrong because although the part of the histogram is true. It is not true that they should be ignored.
d) The outliers differ significantly from the other data but this doesn't make them the minimum and maximum values in a data set and therefore they should not be treated as such.
Therefore, the correct answer is B)
Answer:
commutative property of multiplication
Step-by-step explanation:
The value of the product of the given equation remain the same while the order is reversed
The number sequence 4 × 6 = 6 × 4 is an example of the commutative property of multiplication
Reason:
The given number sentence is 4 × 6 = 6 × 4
Required: The property the number sentence is an example of (represent)
Solution:
The difference between the left and right expression is that the order of the
values being multiplied is changed or reversed (commute)
Therefore, the number sentence states that the value of the multiplication
of two variables remain equal when the places of variables are
interchanged as follows; a × b = b × a
a × b = b × a is an example of commutative property of multiplication
Therefore;
4 × 6 = 6 × 4 is an example of the commutative property of multiplication
Answer:
-15u+5
Step-by-step explanation:
- open up the bracket -15u-5+10
- liketerms together -15u+5
- hence answer is -15u+5
