A basis of a vector space V is a maximal linearly independent
set of vectors in V . Similarly, one can view it as a minimal
spanning set of vectors in V . Prove that any set S ⊆ V spanning a
finite-dimensional vector space V contains a basis of V .
The set of all vectors in R 5 whose coordinates sum to zero
forms a subspace. The following vectors are a generating set for
the space. u1 = (2, −3, 4, −5, 2) u2 = (−6, 9, −12, 15, −6) u3 =
(3, −2, 7, −9, 1) u4 = (2, −8, 2, −2, 6) u5 = (−1, 1, 2, 1 − 3) u6
= (0, −3, −18, 9, 12) u7 = (1, 0, −2, 3, −2) u8 = (2, −1,...
Use one MATLAB statement to generate each of the following
scalars and vectors. (These parts are sequential)
a.) Generate the vector x=(sin5,sin10,sin15,...,sin200) but dont
print
b.)Find the Max value in X and which index has this value. Print
both the index and the value using Disp (so you can use 2
statements)
c.)Find the minimum value x and which index has this value.
Print both the index and the value using Disp (so you can use 2
statements)
d.)Find the...
Given ? = ???+??? + ??? and ? = ???-3?? + ????. Use MATLAB to
find the following: a) ? + ? b) ? ? c) ? × ? d) A unit vector in
the direction of ? − 2? e) ??? f) The component of ? along ?
2. Use MATLAB to convert points ?(11,4,15), ?(10,−14,33) and
?(−33,−14,15) from Cartesian to Cylindrical and Spherical
coordinates.
Use the Gram-Schmidt process to transform the following vectors
into an orthonormal basis of R4:
u1=?(0 2 1 0)?, u2=(?1 −1 0 0) ,u3=?(1 2 0 −1?), u4=?(1 0 0
1?)
can you do this in MATLAB with step by step on how to use the
code
A set of hypothesis and a conclusion are given. Use the valid
argument forms to deduce the conclusion from the hypothesis.
(i) p v q,
(ii) q ->r,
(iii)(p^s) ->t,
(iv) not r,
(v) (not q) -> (u ^ s)
(vi) t
Let A be an infinite set and let B ⊆ A be a subset. Prove:
(a) Assume A has a denumerable subset, show that A is equivalent
to a proper subset of A.
(b) Show that if A is denumerable and B is infinite then B is
equivalent to A.