Given:
Choose a number between 0 and 20.
If the difference is less than 10 then Eric wins.
Let us x is Eric's number. 0 <u><</u> x <u><</u> 20
If Eric wins. |x -7| < 10
|x-7| < 10 → -10 < x-7 < 10 → -10 + 7 < x - 7 + 7 < 10 + 7 → -3 < x < 17
Taking into account that the number must be given between 0 and 20.
0 <u><</u> x <u><</u> 20
-3 < x < 17
→ 0 < x < 16
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
.
To determine the solution of the quadratic equation, use the quadratic formula which states that,
x = ((-b +/- sqrt (b² - 4ac)) / 2a
From the equation, a = 1, b = 14, and c = 112. Substituting these to the quadratic formula,
x = <span>((-14 +/- sqrt (14² - 4(1)(12)) / 2(1) = indeterminate
Thus, the equation does not a real number solution. </span>
Uh oh speggego's im telling teacher lol
Mathematically, yes.
Realistically, no.
The difference in their ages is the parent's age when the child was born.
Let's say that the youngest possible is 12.
Then the ratio would be 10:9 when the parent is 120 and the child is 108.
Not likely.