Question

How to come up with 3x2 linear systems that have infinitely many
solutions?

How do I come up with examples.

Answer #1

How to write matrix as linear system:
3x2 matrix:
(2 2) (x) = (2)
(2 2) (y) = (2)
(1 1) = (1)
How do I know this matrix has infinitely many solutions. Is it
because it is multiplied by an x and y ? Please explain.
We were not taught ranks. So please do not use ranks.

Geometrically, why does a homogenous system of two linear
equations in three variables have infinitely many solutions? If the
system were nonhomogeneous, how many solutions might there be?
Explain this geometrically.

We are all too familiar with linear equations in two variables.
These systems may have no solution, one solution, or infinitely
many. Of course, we can interpret these solutions geometrically as
two parallel lines, two intersecting lines, or two identical lines
in the plane. How does this extend into linear equations in three
variables? If a linear equation in two variables describes a line,
what does a linear equation in three variables describe? Give a
geometric interpretation for the possible...

A: Determine whether the system of linear equations has one and
only one solution, infinitely many solutions, or no solution.
3x - 4y = 9
9x - 12y = 18
B: Find the solution, if one exists. (If there are infinitely
many solutions, express x and y in terms of parameter t. If there
is no solution, enter no solution.)
(x,y)= ?

Determine the value of k such that the following system of
linear equations has infinitely many solutions, and then find the
solutions. (Express x, y, and z in terms of the parameters t and
s.) 3x − 2y + 4z = 9 −9x + 6y − 12z = k k = (x, y, z) =

Use Gauss-Jordan elimination to solve the following systems of
linear equations, or state that there are no solutions.
a)
4?+8?=−4
−3?−6?=5
b)
?+4?−?=8
2?+8?+?=1
you should find that the system has infinitely many solutions.
Introduce a parameter in order to give the general solution. Then
give one particular solution.

A jar contains infinitely many coins which come up Tails with
proba- bility p. A person selects a coin from the jar and flips it
on a table. In the following way, they continue flipping coins
until all coins on the table show Tails: If the last flip came up
Heads, they select a coin from the jar and flip it on the table. On
the other hand, if the last flip came up Tails, they select a coin
from...

Solve the following system of linear equations: 3x2−9x3 = −3
x1−2x2+x3 = 2 x2−3x3 = 0 If the system has no solution, demonstrate
this by giving a row-echelon form of the augmented matrix for the
system. If the system has infinitely many solutions, your answer
may use expressions involving the parameters r, s, and t. You can
resize a matrix (when appropriate) by clicking and dragging the
bottom-right corner of the matrix.

4.
What is a linear Diophantine equation of two variables? How many
solutions can such an equation have? How can the solution(s) be
found?

What are some tips on how to write equations for linear systems
word problems? I need help mostly with coming up with the
equations.

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