When expressing sets, you may write "inf" for infinity and "U" for union.
1 answer:
Answer:
The complement of the given set in interval notation is. It can we written as (-inf,5]U(6,inf).
Step-by-step explanation:
The given set in interval notation is
(−5,6]
It means the set is defined as
If B is a set and U is a universal set, then complement of set B contains the elements of universal set but not the elements of set B.
Here, universal set is R, the set set of all real numbers.
The complement of the given set is
Complement of the given set in interval notation is
Therefore the complement of the given set in interval notation is. It can we written as (-inf,5]U(6,inf).
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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
.