Question

State whether each of the following is true or false:

a) Today we know that the Fermat number 225 + 1 is prime.

b) The Fermat Primes are important in geometry.

c) Fermat’s Last Theorem states that the nonlinear Diophantine equation xn + yn = zn has no nonzero integral solutions for n > 2.

d) The nonlinear Diophantine equation x2+y2 = z2 has no integral solutions.

e) As of 2010, a total of 243 Fermat Numbers are known to be composite. True False

Answer #1

Choose either true or false for each
statement
a. There is a vector [b1 b2] so that the set of solutions to
1
0
1
0
1
0
[ x1, x2 , x3,] =[b1b2] is the z-axis.
b. The homogeneous system Ax=0 has the trivial solution if and
only if the system has at least one free variable.
c. If x is a nontrivial solution of Ax=0, then every entry of x
is nonzero.
d. The equation Ax=b is homogeneous...

7. Answer the following questions true or false and provide an
explanation. • If you think the statement is true, refer to a
definition or theorem. • If false, give a counter-example to show
that the statement is not true for all cases.
(a) Let A be a 3 × 4 matrix. If A has a pivot on every row then
the equation Ax = b has a unique solution for all b in R^3 .
(b) If the augmented...

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