3. Find the mean of each group of numbers:
1 answer:
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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
.
Answer:
Final cost = £779
Step-by-step explanation:
It is given that:
Cost of summer holiday = £650
Amount increased by 11%
Increased cost = 11% of 650
Increased cost =
Increased cost = 0.11 * 650 = £71.50
Amount after increment = 650 + 71.50 = £721.50
Further increase = 8%
Amount = 0.08 * 721.50 = £57.72
Final cost = 721.50 + 57.72 = £779.22
Thus,
Final cost = £779