<span><span>SphereA sphere is the set of all points in space that are a fixed distance from a common point called the center.</span><span>Pyramids<span>A three-dimensional shape with one polygonal base and lateral faces the shape of triangles that meet at a common vertex, called the apex
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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:
I believe the missing number is 65
Step-by-step explanation:
Answer:
3/10 + 4/10
1/2 + 1/5
1/10 + 3/5
Step-by-step explanation:
3/10 + 4/10 = 7/10 (add numerator and keep denominator)
1/2 + 1/5 = 5/10 + 2/10 = 7/10 (use equivalent fractions)
1/10 + 3/5 = 1/10 + 6/10 = 7/10
I hope this helped and please mark me as brainliest!