Answer:
Number of unique treatment combinations = 8
Step-by-step explanation:
Given:
Number of brands = 3
Number of power settings = 2
Number of microwave times = 3
Find:
Number of unique treatment combinations.
Computation:
Number of unique treatment combinations = Number of brands + Number of power settings + Number of microwave times
Number of unique treatment combinations = 3 + 2 + 3
Number of unique treatment combinations = 8
Answer:
C. 10 : 16
Step-by-step explanation:
Attached below
Answer:
(A) Set A is linearly independent and spans
. Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors
, we are to decide which of the given statements is true:
In Matrix
, the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans
. Thus it is basis for
.
24/6=4 students
Pencils divided by how many each receive
Answer:
The answer is B
Step-by-step explanation: