- 4 3/8 - - 1 1/4 help me plz this is so hard
2 answers:
You might be interested in
Answer with explanation:
A basis of a subspace in R³ is the set of vectors that spans the subspace means the set of vectors, and is linearly independent.
The meaning of span is if any set of vectors can be written as linear combination of other vector.
For example , {a, b,c}, {p,q,r} and {x,y,z} are three set of vectors.
If ,{a,b,c} can be wriiten as {pm +x n, q m+y n, r m+z n}, then we say that {a,b,c} spans the set of vectors.
1.
S={(81, 63, 12), (27, 21, 4), (9, 7, 1)}
Writing the set of vectors in matrix form
→Basis of S=1
As all the three vectors are linearly dependent.So, Basis=1.
2.
{(0, 0, 1), (9, 0, 0), (0, 7, 0)}
If you write these three vectors in matrix form , all the three vectors are Linearly Independent.Any of the one vectors can't be written as a linear combination of other
So, Basis =3
3.
{(1, 0, 0), (0, 0, 1), (0, 7, 0)}
All the three vectors are Linearly Independent.
So, Basis=3
4. {(0, 0, 1), (9,7, 0)}
These two vectors can't be written as a linear combination of other.So these two vectors are Independent.So,
Basis=2
5. {9,0,0), (0,7, 0)}
These two vectors can't be written as linear combination of each other.So these two vectors are Independent.So,
Basis=2
Answer:
There are significant differences among the mean tensile strengths for different temperatures.
Step-by-step explanation:
A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.
The hypothesis can be defined as follows:
<em>H₀</em>: There is no difference between the means, i.e. .
<em>Hₐ</em>: There is a significant difference between the means, i.e.at least one of the mean is different.
Use MS-Excel to perform the analysis of variance.
Go to Data → Data Analysis → Anova: Single Factor.
A dialog box will open.
Enter the data and enter Alpha as 0.05.
Press OK.
The output is attached below.
The F-value is, 8.40458.
The <em>p</em>-value of the test is, 0.00139.
Decision Rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
<em>p</em>-value = 0.00139 < <em>α</em> = 0.05
The null hypothesis will be rejected at 5% level of significance.
Concluding that there are differences among the mean tensile strengths for different temperatures.
