Question

Systems of Equations

Given a 3X3 system of equations where all three equations are equal to zero:

1) What is a guaranteed answer to the system?

2) Is this the only answer to the system?

Explain your answers.

Answer #1

you are learning about systems of equations and three methods
for solving them: graphing, substitution, and addition. Compare and
contrast the three methods by discussing the following: Is one
method easier than the others for all systems, or does it depend on
the system? If it depends on the system, how could you tell before
you begin solving the system which solution method would be the
most efficient? How is it possible to tell by inspection (look at
it) whether...

The applications of systems of equations exist in a wide variety
of ways. From our early encounters of a system of equations
involved with cooking ingredients to our numerous adventures into
the business world where system of equations lead to a company's
prosperity, the consistent theme throughout this section is that
systems of equations are intertwined with many aspects of our life.
As a result, you are tasked with providing an example in your own
life where you could have...

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.

For each part below, give an example of a linear system of
three equations in three variables that has the
given property. in each case, explain how you got your answer,
possibly using sketches.
(a) has no solutions
(b) has exactly one solution which is (1, 2, 3).
(c) any point of the line given parametrically be (x, y, z) = (s
− 2, 1 + 2s, s) is a solution and nothing else is.
(d) any point of the...

A linear system of equations Ax=b is known, where A is a matrix
of m by n size, and the column vectors of A are linearly
independent of each other. Please answer the following questions
based on this assumption, please explain it, thank you~.
(1) To give an example, Ax=b is the only solution.
(2) According to the previous question, what kind of inference
can be made to the size of A at this time? (What is the size of...

consider the following systems of rate of change equations
system A : dx/dt=3x(1-x/10)-1/20xy , dy/dt=-5y+xy/20, system B:
dx/dt=3x-xy/100, dy/dt=15y(1-y/17)+25xy. in both of these systems,x
and y refer to the number of two different species at time t.In
particular, in one of these systems, the prey is large animals and
the predators are small animals, such as piranhas and humans. Thus
it takes many predators to eat one prey, but each prey eaten is a
tremendous benefit for the predator population....

x1-5x2+x3+3x4=1
2x1-x2-3x3-x4=3
-3x1-3x3+7x3+5x4=k
1 ) There is exactly one real number k for which the system has
at least one solution; determine this k and describe all solutions
to the resulting system.
2 ) Do the solutions you found in the previous part form a
linear subspace of R4?
3 ) Recall that a least squares solution to the system of equations
Ax = b is a vector x minimizing the length |Ax=b| suppose that
{x1,x2,x3,x4} = {2,1,1,1}
is a...

Two systems of equations are given below. For each system,
choose the best description of its solution. If applicable, give
the solution.
-x + 2y = -4
x- 2y = 4
*The system has no solution
*The system has a unique solution (x,y) = ?,?
*The system has infinitely many solutions. They must satisfy the
following equation: y= ?
x - 3y = 6
-x + 3y = 6
*The system has no solution
*The system has a unique solution...

Matlab: Solve the following set of simultaneous equations.
Remember, the system cannot be solved if the determinant of the
coefficient matrix is zero. Use if statements to only display the
results if the determinant is not zero
a) 3x1 + 2x2 + 4x3 = 5
2x1 + 5x2 + 3x3 = 17
7x1 + 2x2 + 2x3 = 11
b) x – y – z = 0
30x + 40y = 12
30x + 50z = 12
c) 4x +...

Use Gauss-Jordan row reduction to solve the given system of
equations. HINT [See Examples 1-6.] (If there is no solution, enter
NO SOLUTION. If the system is dependent, express your answer in
terms of x, where
y =
y(x).)
9x
−
5y
=
4
45x
−
25y
=
20

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