Question

The arbitrary constant and showing for example why a 2x3 linear
system doesn't have a unique solutions confuses me:

Apparently: 2x3 there are 2 equation and 3 variable.. I don't know
where to go from here.

Can I take any 2x3 matrix to show that a linear system doesn't have
a unique solution?

Answer #1

Is it possible to have an inconsistent 2x3 linear system, 3x2,
3x4, 4x3 ?
Explain why our why not. What is meant by inconsistent.
I do not know any big words like rank. None of those are in my
notes.
Please explain in a way that would make sense for a person fresh
out of high school.

For each statement below, either show that the statement is true
or give an example showing that it is false. Assume throughout that
A and B are square matrices, unless otherwise specified.
(a) If AB = 0 and A ̸= 0, then B = 0.
(b) If x is a vector of unknowns, b is a constant column vector,
and Ax = b has no solution, then Ax = 0 has no solution.
(c) If x is a vector of...

4. Suppose that we have a linear system given in matrix form as
Ax = b, where A is an m×n matrix, b is an m×1 column vector, and x
is an n×1 column vector. Suppose also that the n × 1 vector u is a
solution to this linear system. Answer parts a. and b. below.
a. Suppose that the n × 1 vector h is a solution to the
homogeneous linear system Ax=0.
Showthenthatthevectory=u+hisasolutiontoAx=b.
b. Now, suppose that...

A system of linear equations is said to be homogeneous if the
constants on the right-hand side are all zero. The system
2x1 − x2 + x3 + x4 = 0
5x1 + 2x2 − x3 − x4 = 0
−x1 + 3x2 + 2x3 + x4 = 0
is an example of a homogeneous system. Homogeneous systems
always have at least one solution, namely the tuple consisting of
all zeros: (0, 0, . . . , 0). This solution...

LAB 3.1 Bifurcations in Linear Systems
In Chapter 3, we have studied techniques for solving linear
systems. Given the coefﬁcient matrix for the system, we can use
these techniquesto classify the system, describe the qualitative
behavior of solutions, and give a formula for the general solution.
In this lab we consider a two-parameter family of linear systems.
The goal is to better understand how different linear systems are
related to each other, or in other words, what bifurcations occur
in...

Solve the linear systems that abides by the following rules.
Show all steps.
I. The first nonzero coefficient in each equation is one.
II. If an unknown is the first unknown with a nonzero
coefficient in some equation, then that unknown doesn't appear in
other equations.
II. The first unknown to appear in any equation has a larger
subscript than the first unknown in any preceding equation.
a. x1 + 2x2 - 3x3 + x4 = 1.
-x1 - x2...

Have to make a linear regression graph with this data showing
that when Real Madrid's best player is there (2017-18) they have
higher attendance than when he left (2018-19):
2018-2019
Game Real Madrid Attendance Real Madrid
Stadium Capacity
1 48346 81044
2 59255 81044
3 68034 81044
4 78562 81044
5 63762 81044
6 68120 81044
7 69653 81044
8 55229 81044
9 53412 81044
10 68507 81044
2017-2018
Game Real Madrid Attendance Real Madrid
Stadium...

Prove that for a square n ×n matrix A, Ax = b (1) has one and
only one solution if and only if A is invertible; i.e., that there
exists a matrix n ×n matrix B such that AB = I = B A.
NOTE 01: The statement or theorem is of the form P iff Q, where
P is the statement “Equation (1) has a unique solution” and Q is
the statement “The matrix A is invertible”. This means...

This is not for an assignment, but for my own
understanding and I was wondering if anyone would be able to assist
me with understanding.
Consider a non-trivial trajectory where the velocity &
acceleration of some charged particle are non-zero.
If i were wanting to plot the electric and magnetic field, how
would I go about making the equation to do so? Would you be able to
give me an example?
If I wanted to convert a 2 dimensional plot...

Your discussion response for this unit will consist of two
parts.
First, create 3 equations of the form , where a, b, c,
and d are constants (integers between – 5 and 5). For
example, . Perform row operations on your system to obtain a
row-echelon form and the solution.
Go to the 3D calculator website GeoGebra:
www.geogebra.org/3d?lang=pt and enter each of the equations.
After you have completed this first task, choose
one of the following to complete your discussion...

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