Question

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.

Answer #1

The augmented matrix represents a system of linear equations in
the variables x and y.
[1 0 5. ]
[0 1 0 ]
(a) How many solutions does the system have: one, none, or
infinitely many?
(b) If there is exactly one solution to the system, then give
the solution. If there is no solution, explain why. If there are an
infinite number of solutions, give two solutions to the system.

Let A be a n × n matrix, and let the system of linear equations
A~x = ~b have infinitely many solutions. Can we use Cramer’s rule
to find x1? If yes, explain how to find it. If no, explain why
not.

How to come up with 3x2 linear systems that have infinitely many
solutions?
How do I come up with examples.

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.

Find the values of a and b for which the following system of
linear equations is (i) inconsistent; (ii) has a unique solution;
(iii) has infinitely many solutions. For the case where the system
has infinitely many solutions, write the general solution.
x + y + z = a
x + 2y ? z = 0
x + by + 3z = 2

1. a) Find the solution to the system of linear equations using
matrix row operations. Show all your work.
x + y + z = 13
x - z = -2
-2x + y = 3
b) How many solutions does the following system have? How do you
know?
6x + 4y + 2z = 32
3x - 3y - z = 19
3x + 2y + z = 32

The augmented matrix below represents a system of linear
equations associated with a real world prob-
lem. The augmented matrix has already been completely row
reduced.
1 0 6 12 0 1 −2 0 0000
(a) Use the reduced matrix to write down the parametric solution
for the system as a point (x, y, z).
(b) Assuming that x, y, and z represent the number of whole
items, determine how many “actual” solutions this system has, and...

2. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions.In the latter case,present
the solutions in parametric form
x+2y+3z=7
-12z=24
-10y-5z=-40

4. Solve the system of linear equations by using the
Gauss-Jordan (Matrix) Elimination Method. No credit in use any
other method. Use exactly the notation we used in class and in the
text. Indicate whether the system has a unique solution, no
solution, or infinitely many solutions. In the latter case, present
the solutions in parametric form.
3x + 6y + 3z = -6
-2x -3y -z = 1
x +2y + z = -2

4. [10] Consider the system of linear equations
x + y + z = 4
x + y + 2z = 6
x + y + (b2 − 3)z = b + 2
where b is an unspecified real number. Determine, with
justification, the values of b (if any) for which the system
has
(i) no solutions;
(ii) a unique solution;
(ii) infinitely many solutions.

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