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 .
8/3=3x (cross multiplied to get this)
X=8/9 (divided both sides by 3)
Hope this helps :)
(0.9)* (1.5+5.8)
First, Add the values to the right. You get (0.9) * (7.3)
Multiply 9 and 73 to get 730 -73, which is 700-43, 660 - 3, which is 657.
Divide by 100 by moving the decimal point to get 6.57 as your final answer.
Hope that helped!
Answer:
see explanation
Step-by-step explanation:
(a)
2x + 10 ← factor out 2 from each term
= 2(x + 5)
(b)
5x - 15 ← factor out 5 from each term
= 5(x - 3)
(c)
8x + 6 ← factor out 2 from each term
= 2(4x + 3)
(d)
12x - 8 ← factor out 4 from each term
= 4(3x - 2)
Answer:
Mean = 50
Step-by-step explanation:
<em>Step 1: Write the mean formula</em>
Mean = sum of data/ total number of data
<em>Step 2: Calculate the sum of data</em>
35 + 40 + 45 +50 + 55 + 60 + 65 = 350
<em>Step 3: Find the total number of data</em>
Total number of data = 7
<em>Step 4: Calculate the mean</em>
Mean = sum of data/ total number of data
Mean = 350/7
Mean = 50
Therefore, the mean of this data is 50.
!!
