Question

Set up the system of equations and then solve it by using an
inverse matrix.

A trust account manager has $2,000,000 to be invested in three
different accounts. The accounts pay 6%, 8%, and 10%, and the goal
is to earn $168,000 with the amount invested at 10% equal to the
sum of the other two investments. To accomplish this, assume that
*x* dollars are invested at 8%, *y* dollars at 10%,
and *z* dollars at 6%. Find how much should be invested in
each account to satisfy the conditions.

8% rate | $ |

10% rate | $ |

6% rate | $ |

Answer #1

Solve the system of equations by using the inverse of the
coefficient matrix.
{ ? + ? − ? = 0
3? − ? = −8
2? − 3? + 4? = −6

Set up the system of equations and then solve it by using an
inverse matrix.
A manufacturer of table saws has three models (Deluxe, Premium, and
Ultimate) that must be painted, assembled, and packaged for
shipping. The table gives the number of hours required for each of
these operations for each type of table saw.
Deluxe
Premium
Ultimate
Painting
1.6
2
2.4
Assembly
2
3
4
Packaging
0.5
0.5
1
(a) If the manufacturer has 96 hours available per day...

Use an inverse matrix to solve (if possible) the system of
linear equations. (If there is no solution, enter NO SOLUTION.)
4x
−
2y
+
3z
=
−16
2x
+
2y
+
5z
=
−30
8x
−
5y
−
2z
=
30

Solve the system of equations using an inverse matrix
-4x-2y+z= 6
-x-y-2z= -3
2x+3y-z= -4
Choose one:
a. (-1, 0, -2)
b. (1, 0, -2)
c. (1, 0, 2)
d. (-1, 0, 2)

Solve the following system of equations by using the inverse of
the coefficient matrix.
7x?y+4z=?3
?3y+8z=?20
-2x+4y+5z=-42

use matrix manipulation to solve for a, b, and c. Set up a
matrix equation for AX=B based on the system of equations below,
where X is a matrix of the variables a, b and c. Then, use
Gauss-Jordan elimination to find the inverse of A. Finally, use
your results to write the equation of the parabola. Show your work
and final equation in the space provided. 9a+3b+c=8 ,
25a+5b+c=20/3, 36a+6b+c=5

Write the system of equations as an augmented matrix. Then solve
the system by putting the matrix in reduced row echelon form.
x+2y−z=-10
2x−3y+2z=2
x+y+3z=0

Solve system of equations using matrices. Make a 4x4 matrix and
get the diagonal to be ones and the rest of the numbers to be
zeros
2x -3y + z + w = - 4
-x + y + 2z + w = 3
y -3z + 2w = - 5
2x + 2y -z -w = - 4

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=?

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

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