- 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, that 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
-
![{\displaystyle {}f=a+bX+cX^{2}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8049b64104867c582e007106c9abfb54ea2ce680)
with
,
such that the following conditions hold.
-
Find a
polynomial
-
![{\displaystyle {}f=a+bX+cX^{2}+dX^{3}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a15cb632f45ca47ff084ba7da6076d1323b9a529)
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
-
![{\displaystyle {}z=a+b{\mathrm {i} }\neq 0\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ce7472e7d52df5ea4c48755b3cb65ce447f2c81)
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 with 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
-
![{\displaystyle {}f=a+bX+cX^{2}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8049b64104867c582e007106c9abfb54ea2ce680)
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?