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:
NO. Alex was wrong.
The total dive distance is 21 + 17 = 38 feet
Step-by-step explanation:
Alex was wrong because his direction of diving is from above the water through the surface of the water to under the water.
So his direction of travelling is not opposite but the same.
Therefore the total distance traveled by Alex = distance traveled from the diving board to the water surface + distance traveled from the water surface to down below the water
Distance traveled from the diving board to the water surface = 21 feet
Distance traveled from the water surface down below the water = 17 feet
Total distance traveled by Alex = 21 feet + 17 feet
= 38 feet.
Thus, Alex was wrong because the the total distance traveled by Alex was 38 feet.
3 out of 25 = 12 out of 100
3 out of 50 = 6 out of 100
2 out of 25 = 8 out of 100
12 + 6 + 8 = 26
100 - 26 = 74%
Answer:
Conquered Egypt?
Step-by-step explanation:
<h3>
Answer: x = 21</h3>
Explanation:
The two angles shown combine to 180 degrees because the angles form a straight line.
(3x+18)+(4x+15) = 180
7x+33 = 180
7x = 180-33
7x = 147
x = 147/7
x = 21
