If there is 2 digits and 7 numbers the combos would be:
1,1 2,1 3,1 4,1 5,1 6,1 7,1
1,2 2,2 3,2 4,2 5,2 6,2 7,2
1,3 2,3 3,3 4,3 5,3 6,3 7,3
1,4 2,4 3,4 4,4 5,4 6,4 7,4
1,5 2,5 3,5 4,5 5,5 6,5 7,5
1,6 2,6 3,6 4,6 5,6 6,6 7,6
1,7 2,7 3,7 4,7 5,7 6,7 7,7
Therefore there are 49 possible combinations :)
Answer:
f(3) = 4
f(-7) = -26
Step-by-step explanation:
Hi there!

To find f(3), replace every x with 3:

Therefore, f(3)=4.

To find f(-7), replace every x with -7:

Therefore, f(-7)=-26.
I hope this helps!
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
.