nd the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM. 9) A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. 1 9) sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank inv each? Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount inve: mortgages. A) x + y - z = 11,400 x - y + 9z = 22 8x +y +z = 124,000 C) x + y - z = 0 x + y + z = 124,000 0.09x + 0.08y + 0.1z = 11,400 B) x + y - z = 0 x + y +z= 124,000 9x + 8y + z = 11,400 D) x + y + z =0 x + y - 9z = 124,000 0.1x + 0.08y - 0.09z = 11,400
nd the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM. 9) A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. 1 9) sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank inv each? Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount inve: mortgages. A) x + y - z = 11,400 x - y + 9z = 22 8x +y +z = 124,000 C) x + y - z = 0 x + y + z = 124,000 0.09x + 0.08y + 0.1z = 11,400 B) x + y - z = 0 x + y +z= 124,000 9x + 8y + z = 11,400 D) x + y + z =0 x + y - 9z = 124,000 0.1x + 0.08y - 0.09z = 11,400
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Matrix and Systems of Equations Practice Problems**
**MULTIPLE CHOICE: Choose the one alternative that best completes the statement or answers the question.**
8) Only one of the following augmented matrices of a linear system is in reduced form. Choose the one that is in reduced form.
A)
\[
\begin{bmatrix}
0 & 1 & -2 \\
1 & 0 & -3
\end{bmatrix}
\]
B)
\[
\begin{bmatrix}
1 & 0 & -2 \\
0 & 0 & 0 \\
0 & 1 & -1
\end{bmatrix}
\]
C)
\[
\begin{bmatrix}
1 & 4 & 0 & 4 \\
0 & 1 & -4 \\
0 & 0 & 0
\end{bmatrix}
\]
D)
\[
\begin{bmatrix}
1 & 0 & -2 & 2 \\
0 & 0 & 1 & 3
\end{bmatrix}
\]
**Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.**
9) A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank invest in each?
Let \( x \) represent the amount invested in bonds, \( y \) the amount invested in CDs, and \( z \) the amount invested in mortgages.
A)
\[
\begin{align*}
x + y - z &= 11,400 \\
x - y + 9z &= 22 \\
8x + y + z &= 124,000
\end{align*}
\]
B)
\[
\begin{align*}
x - y - z &= 0 \\
x + y + z &= 124,000 \\
9x + 8y + z &= 11,400
\end{align*}
\]
C)
\[
\begin{align*}
x + y - z &= 0 \\
x + y + z &= 124,000 \\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ad954f6-3e43-4185-98a8-84783e08c6bc%2F76df35b0-1d89-4bbb-8248-a9d7dbe6249f%2F6adrb6q_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix and Systems of Equations Practice Problems**
**MULTIPLE CHOICE: Choose the one alternative that best completes the statement or answers the question.**
8) Only one of the following augmented matrices of a linear system is in reduced form. Choose the one that is in reduced form.
A)
\[
\begin{bmatrix}
0 & 1 & -2 \\
1 & 0 & -3
\end{bmatrix}
\]
B)
\[
\begin{bmatrix}
1 & 0 & -2 \\
0 & 0 & 0 \\
0 & 1 & -1
\end{bmatrix}
\]
C)
\[
\begin{bmatrix}
1 & 4 & 0 & 4 \\
0 & 1 & -4 \\
0 & 0 & 0
\end{bmatrix}
\]
D)
\[
\begin{bmatrix}
1 & 0 & -2 & 2 \\
0 & 0 & 1 & 3
\end{bmatrix}
\]
**Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.**
9) A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank invest in each?
Let \( x \) represent the amount invested in bonds, \( y \) the amount invested in CDs, and \( z \) the amount invested in mortgages.
A)
\[
\begin{align*}
x + y - z &= 11,400 \\
x - y + 9z &= 22 \\
8x + y + z &= 124,000
\end{align*}
\]
B)
\[
\begin{align*}
x - y - z &= 0 \\
x + y + z &= 124,000 \\
9x + 8y + z &= 11,400
\end{align*}
\]
C)
\[
\begin{align*}
x + y - z &= 0 \\
x + y + z &= 124,000 \\
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