257,650 rounded to the nearest hundred is 257,700 because it is right at the border (50) we have to round up.
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
.
(0,-6), (6, -3), and (6,-6)
If you plot them on a graph there are only two point options (in green and purple) since it's a right triangle but you have to use the one that has -6 as the y value
Answer:
The area of the square base is 100 in.2.
The area of each triangular face is 40 in.2.
Alexander will need 260 in.2 of paint.
Step-by-step explanation:
I dan't have an explanation I just guessed.