I don't think any of them exist. the only ones I can think of make my feel there are any others
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 ![A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right)](https://tex.z-dn.net/?f=A%3D%20%5Cleft%28%5Cbegin%7Barray%7D%7B%5Bc%5D%5Bc%5D%5Bc%5D%5Bc%5D%7D1%20%26%200%20%26%200%20%26%200%5C%5C%200%20%26%201%20%26%200%20%26%201%5C%5C%200%20%26%200%20%26%201%20%26%201%5Cend%7Barray%7D%20%5Cright%29%20)
, we are to decide which of the given statements is true:
In Matrix ![A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right)](https://tex.z-dn.net/?f=A%3D%20%5Cleft%28%5Cbegin%7Barray%7D%7B%5Bc%5D%5Bc%5D%5Bc%5D%5Bc%5D%7D%281%29%20%26%200%20%26%200%20%26%200%5C%5C%200%20%26%20%281%29%20%26%200%20%26%201%5C%5C%200%20%26%200%20%26%20%281%29%20%26%201%5Cend%7Barray%7D%20%5Cright%29%20)
, 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:
For 3x^2+4x+4=0
Discriminant= = -32
The solutions are
(-b+√x)/2a= (-2+2√-2)/3
(-b-√x)/2a= (-2-2√-2)/3
For 3x^2+2x+4=0
Discriminant= -44
The solutions
(-b+√x)/2a= (-1+√-11)/3
(-b-√x)/2a= (-1-√-11)/3
For 9x^2-6x+2=0
Discriminant= -36
The solutions
(-b+√x)/2a= (1+√-1)/3
(-b-√x)/2a= (1-√-1)/3
Step-by-step explanation:
Formula for the discriminant = b²-4ac
let the discriminant be = x for the equations
The solution of the equations
= (-b+√x)/2a and = (-b-√x)/2a
For 3x^2+4x+4=0
Discriminant= 4²-4(3)(4)
Discriminant= 16-48
Discriminant= = -32
The solutions
(-b+√x)/2a =( -4+√-32)/6
(-b+√x)/2a= (-4 +4√-2)/6
(-b+√x)/2a= (-2+2√-2)/3
(-b-√x)/2a =( -4-√-32)/6
(-b-√x)/2a= (-4 -4√-2)/6
(-b-√x)/2a= (-2-2√-2)/3
For 3x^2+2x+4=0
Discriminant= 2²-4(3)(4)
Discriminant= 4-48
Discriminant= -44
The solutions
(-b+√x)/2a =( -2+√-44)/6
(-b+√x)/2a= (-2 +2√-11)/6
(-b+√x)/2a= (-1+√-11)/3
(-b-√x)/2a =( -2-√-44)/6
(-b-√x)/2a= (-2 -2√-11)/6
(-b-√x)/2a= (-1-√-11)/3
For 9x^2-6x+2=0
Discriminant= (-6)²-4(9)(2)
Discriminant= 36 -72
Discriminant= -36
The solutions
(-b+√x)/2a =( 6+√-36)/18
(-b+√x)/2a= (6 +6√-1)/18
(-b+√x)/2a= (1+√-1)/3
(-b-√x)/2a =( 6-√-36)/18
(-b-√x)/2a= (6 -6√-1)/18
(-b-√x)/2a= (1-√-1)/3
Answer:
<h2>10</h2>
Step-by-step explanation:
Given the expression 
. To find the product of this two values, the following steps must be followed.
According to one of the law of indices, 
The product is 10
1/8 = 0.125
23.125 x 17 gallons = 393.125
393.125 = 393 1/8 miles
