- Warm-up-exercises
and are the members of one family. In this case, is three times as old as
and
together, is older than , and is older than , moreover, the age difference between and is twice as large as the difference between and . Furthermore, is seven times as old as , and the sum of the ages of all family members is equal to the paternal grandmother's age, which is .
a) Set up a linear system of equations that expresses the conditions described.
b) Solve this system of equations.
Kevin pays € for a winter bunch of flowers with snowdrops and mistletoes, and Jennifer pays € for a bunch with snowdrops and mistletoes. How much does a bunch with one snowdrop and mistletoes cost?
We look at a clock with hour and minute hands. Now it is 6 o'clock, so that both hands have opposite directions. When will the hands have opposite directions again?
Find a
polynomial
-
with
,
such that the following conditions hold.
-
Find a
polynomial
-
with
,
such that the following conditions hold.
-
Exhibit a linear equation for the straight line in , which runs through the two points
and .
Determine an equation for the secant of the function
-
to the points
and .
Determine a linear equation for the plane in , where the three points
-
lie.
Given a
complex number
-
find its inverse complex number with the help of a real system of linear equations, with two equations in two variables.
Solve, over the
complex numbers,
the
linear system
of equations
-
Let be the field with two elements. Solve in the
inhomogeneous linear system
-
Show by an example that the linear system given by three equations I, II, III is not equivalent to the linear system given by the three equations I-II, I-III, II-III.
- Hand-in-exercises
Solve the following system of inhomogeneous linear equations.
-
Consider in the two planes
-
Determine the intersecting line .
Determine a linear equation for the plane in , where the three points
-
lie.
Find a polynomial
-
with
,
such that the following conditions hold.
-
We consider the linear system
-
over the real numbers, depending on the parameter
.
For which does the system of equations have no solution, one solution, or infinitely many solutions?