What is the area of the tile?
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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
.
Probability between z = 0 and z = 3.01 is given by
P(0<z<3.01) = P(z<3.01) - P(z<0)
Reading from the z-table, we have
P(z<0) = 0.5
P(z<3.01) = 0.9987
Hence, P(0<z<3.01) = 0.9987 - 0.5 = 0.4987
P(0<z<3.01) = P(z<3.01) - P(z<0)
Reading from the z-table, we have
P(z<0) = 0.5
P(z<3.01) = 0.9987
Hence, P(0<z<3.01) = 0.9987 - 0.5 = 0.4987