Question

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)= ?

Answer #1

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) =

1)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express your answer in terms
of the parameters t and/or s.)
x1
+
2x2
+
8x3
=
6
x1
+
x2
+
4x3
=
3
(x1,
x2, x3)
=
2)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express...

PLEASE WORK THESE OUT!!
A) Solve the system of linear equations using the Gauss-Jordan
elimination method.
2x
+
10y
=
−1
−6x
+
8y
=
22
x,y=_________
B) If n(B) = 14, n(A ∪
B) = 30, and n(A ∩ B) = 6, find
n(A).
_________
C) Solve the following system of equations by graphing. (If
there is no solution, enter NO SOLUTION. If there are infinitely
many solutions, enter INFINITELY MANY.)
3x
+
4y
=
24
6x
+
8y...

his is a linear algebra problem
Determine the values of a for which the system has no
solutions, exactly one solution, or infinitely many solutions.
x + 2y - 2z = 3
3x - y + 2z = 3
5x + 3y + (a^2 - 11)z = a + 6
For a = there is no solution.
For a = there are infinitely many solutions.
For a ≠ ± the system has exactly one solution.

Solve the system of linear equations. If the system has an
infinite number of solutions, set w = t and solve for x, y, and z
in terms of t.)
x + y + z + w = 6
2x+3y - w=6
-3x +4y +z + 2w= -1
x + 2y - z + w = 0
x, y, z, w=?

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

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations. Indicate whether
the system has a unique solution, infinitely many solutions, or no
solution. Clearly write the row operations you use. (a) (5 points)
x + y + z = 6 2x − y − z = 3 x + 2y + 2z = 0 (b) (5 points) x − 2y
+ z = 4 3x − 5y + 3z = 13 3y − 3z =...

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

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.

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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