# Tutor profile: Reanna S.

## Questions

### Subject: Linear Algebra

Let V be a vector space over a field F and let $$ S = { a1, a2, a3,...ak } $$ {k is a set of Z^+} be a finite subset of vectors in V. Complete the following statements: 1. S is said to be linearly independent iff _____________________ 2. S is said to span V iff ___________________ 3. S is a basis for V iff ___________________

1. S is said to be linearly independent iff every equation of the form $$ a1α1 + a2α2 +.....akαk = θ $$ 2. S is said to span V iff every vector in V can be written as a linear combination of the vectors in S. 3. S is a basis for V iff S is linearly independent and spans.

### Subject: Applied Mathematics

The pilot of a hot air balloon has mass 85 kg. As the balloon leaves the ground, the normal contact force on the pilot from the floor of the balloon immediately increased to 901 N and remains at this value for the first stage of the ascent. Calculate the acceleration of the balloon in this stage of its motion.

$$ Mass of pilot= 85 kg $$ $$ Therefore, weight of pilot= 85 kg x 10 (using gravity as 10 N) $$ $$ = 850 N $$ As balloon leaves the ground, normal contact force= 901 N Using Newton's Second Law, $$ 901 N - 850 N= 85a $$ $$ 51= 85a $$ $$ a= 0.6 ms^-2 $$

### Subject: Partial Differential Equations

$$ Uxy= 3x - 7y^2 $$

To solve the above question, we integrate with respect to x say, treating y as a constant. Hence, $$ Uy= 3x^2/ 2 - 7xy^2 $$

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