Question

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) =

Answer #1

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)= ?

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...

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

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=?

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.

Determine the value of k for which the following system has no
solutions. Write answer as an integer or a fraction in lowest
terms.
x+y+4z=0
x+2y?4z=1
?2x?y+kz=2

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

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 =...

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

Exercise 2.4 Assume that a system Ax = b of linear equations has
at least two distinct solutions y and z.
a. Show that xk = y+k(y−z) is a solution for every
k.
b. Show that xk = xm implies k = m. [Hint:
See Example 2.1.7.]
c. Deduce that Ax = b has infinitely many solutions.

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