Question

Solve the system of equations by using the inverse of the coefficient matrix.

{ ? + ? − ? = 0

3? − ? = −8

2? − 3? + 4? = −6

Answer #1

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

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)

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...

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

Consider the following system of equations.
3x
−
2y
=
b1
4x
+
3y
=
b2
(a) Write the system of equations as a matrix equation.
x
y
=
b1
b2
(b) Solve the system of equations by using the inverse of the
coefficient matrix.(i) where
b1 = −6, b2 = 11
(x, y) =
(ii) where
b1 = 4, b2 = −2
(x, y) =

Consider the following system of equations.
x1- x2+ 3x3 =2
2x1+ x2+ 2x3 =2
-2x1 -2x2 +x3 =3
Write a matrix equation that is equivalent to the system of
linear equations.
(b) Solve the system using the inverse of the coefficient
matrix.

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

Use the Gauss-Jordan method with pivoting to find the
inverse of the coefficient matrix for the system of equations
given. Hint: Keep values as fractions rather than
estimating using decimal points throughout. When reporting your
answer, convert to decimal form.
Approximately halfway through calculating the inverse,
just before multiplying Row 3 by a scalar so that A(3,3) becomes 1,
what is the value of A(3,3)? Answer is 0.1
On the last calculation, just before multiplying Row 1
by a scalar so that...

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

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