Determine whether w is in the span of the given vectors v1; v2; : : : vn
. If your answer is yes, write w as a linear combination of the vectors v1; v2; : : : vn and enter the coefficients as entries of the matrix as instructed is given below
Explanation:
1.Vector to be in the span means means that it contain every element of said vector space it spans. So if a set of vectors A spans the vector space B, you can use linear combinations of the vectors in A to generate any vector in B because every vector in B is within the span of the vectors in A.
2.And thus v3 is in Span{v1, v2}. On the other hand, IF all solutions have c3 = 0, then for the same reason we may never write v3 as a sum of v1, v2 with weights. Thus, v3 is NOT in Span{v1, v2}.
3.In the theory of vector spaces, a set of vectors is said to be linearly dependent if at least one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent.
4.Given a set of vectors, you can determine if they are linearly independent by writing the vectors as the columns of the matrix A, and solving Ax = 0. If there are any non-zero solutions, then the vectors are linearly dependent. If the only solution is x = 0, then they are linearly independent.
Answer:
Explanation:
By an adequate application of the Principle of Energy Conservation, the escalator need energy to elevate from to the bottom to the top. Hence:
An expression for power needed is found by deriving the equation with respect to time:
The minimum power is found by substituting known inputs:
Yes all aircraft near collision events must be notified to the FAA and Air Traffic Control
Answer:
The heat transferred to water equals 1600 kJ
Explanation:
By the conservation of energy we have
All the kinetic energy of the moving vehicle is converted into thermal energy
We know that kinetic energy of a object of mass 'm' moving with a speed of 'v' is given by
Thus
Thus the heat transferred to water equals 
Answer:
v = 21.409 m/s
Explanation:
Given data:
Total weight of the platform and weight together, W = 900 N
Diameter of the water jet = 5 cm = 0.05 m
Now,
the force exerted by the water jet is balancing the platform
also,
Force exerted by the water jet = ρAv²
where,
ρ is the density of the water = 1000 kg/m³
A is the area of the outlet of the jet = 
or
A = 0.00196 m²
v is the velocity of the jet
thus,
W = ρAv²
or
900 = 1000 × 0.00196 × v²
or
v = 21.409 m/s
Hence, the velocity of the jet is 21.409 m/s
