Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
The answer is 9 cm
Hope that helps! :)
Answer:
18
Step-by-step explanation:
First I'm making all mixed numbers improper fractions.
Base recipe: 12 muffins = 2/3 milk + 7/4 flour + 1/4 coconut + 3/4 apple
Change: 9/8 apple
On second look, I ddn't need to do that except for the last one, the change in apple. When increasing things proportionally you basically multiply everything by the same number. A simple example.
Say a recipe made 10 of something with 1 of ingredient A and 2 of ingredient B. Well, what if you made the recipe twice? that would be 20 things from 2 of A and 4 of B. This is the same as changing the recipe to make double. It works if you halve things as well, or multiply by any number or fraction.
So the point is, we changed the amount of apples. We want to know how much we changed it by, then that much is how much the total number of muffins changes. So if we doubled apples the muffins would double, but I don't think it's that simple.
Started at 3/4 cup of chopped apple and increased to 9/8 cups. We want to know what to multiiply by to do this. So we set up a simple algebraic equation.
(3/4)x = 9/8
where x is what we multiply by. Now, to do this you could do one step, divide by 3/4 or you could do it in two steps, multiply both sides by 4 then divide by 3. Or the other way around. Either way you will get the same number.
(3/4)x = 9/8
3x = 9/2
x = 3/2
And you can (and should) double check
(3/4)x = 9/8
(3/4)(3/2) = 9/8
9/8 = 9/8
Yay! If you don't gt fraction multiplication let me know. But the recipie is an increase of 3/2 or 1.5, so there will be 1.5 as many muffins.
12*1.5 = 12(3/2) = 18
Answer:
6 ways.
There are one red, one blue and one green maker. So there are 3 markers they are in 3! = 3×2 = 6 ways.
Please mark brainliest! <3
