Question 1

Solve the system graphically. Round answers to the nearest hundredth.
$\begin{array}{l}
y=4-7 x^{2}+3 x^{3} \
y=-1+2 x
\end{array}$

Accepted Answer

(-0.84,-2

Question 2

Solve the system graphically.
$\begin{aligned}
8 x^{2}+32 y^{2} &=256 \
x &=2 y
\end{aligned}$

Accepted Answer

(4,2),(-4,-2) 
11ec

Question 3

Tell what elementary row operation can be applied to
$\left[\begin{array}{rrrr}
3 & 6 & -2 & 5 \
4 & 7 & 5 & -2 \
-3 & 2 & 0 & 3
\end{array}\right]$
to obtain $\left[\begin{array}{rrrr}
15 & 27 & 13 & -1 \
4 & 7 & 5 & -2 \
-3 & 2 & 0 & 3
\end{array}\right]$

Accepted Answer

A)  $5 R_{1}$ 
B)  $3 R_{2}+R_{1}$ 
C)  $3 R_{1}+R_{2}$ 
D)  $3 R_{2}-R_{3}$ 
A)  $5 R_{1}$ 
B)  $3 R_{2}+R_{1}$ 
C)  $3 R_{1}+R_{2}$ 
D)  $3 R_{2}-R_{3}$

Question 4

Find $A^{-1}$ of the matrix $A=\left[\begin{array}{rrr}
1 & 0 & 0 \
-2 & 1 & 5 \
4 & 0 & 1
\end{array}\right]$

Accepted Answer

None

Question 5

Find the determinant of the matrix
$B=\left[\begin{array}{rrr}
2 & -1 & 4 \
3 & 1 & -2 \
1 / 2 & 4 & 5
\end{array}\right]$
Does matrix  B  have an inverse?

Accepted Answer

The answer of Find the determinant of the matrix
\(B=\left[\begin{array}{rrr}
2 &...

Question 6

Using matrix $A=\left[\begin{array}{rrr}
3 & 7 & 4 \
2 & -1 & 6
\end{array}\right]$ and $B=\left[\begin{array}{rrr}
-1 & 5 & 2 \
7 & 10 & 1 \
-2 & 5 & -1
\end{array}\right]$ which of the following is a true statement?

Accepted Answer

A)  Matrix  A  has an inverse. 
B)  $A+B=\left[\begin{array}{rrr}
2 & 12 & 6 \
9 & 9 & 7 \
-2 & 5 & -1
\end{array}\right]$ 
C)   AB  exists and  BA  does not exist. 
D)   BA  exists and  AB  does not exist. 
A)  Matrix  A  has an inverse. 
B)  $A+B=\left[\begin{array}{rrr}
2 & 12 & 6 \
9 & 9 & 7 \
-2 & 5 & -1
\end{array}\right]$ 
C)   AB  exists and  BA  does not exist. 
D)   BA  exists and  AB  does not exist.

Question 7

Solve the system by elimination.
$\begin{aligned}
x-2 y &=4 \
x+y &=1
\end{aligned}$

Accepted Answer

The answer of Solve the system by elimination.
\(\begin{aligned}
x-2 y &=4...

Question 8

Find the solution to the system of equations represented by the augmented matrix.
$\left[\begin{array}{rrrr}
1 & 3 & -4 & -13 \
0 & 1 & 2 & 4 \
0 & 0 & 1 & 3
\end{array}\right]$

Accepted Answer

The answer of Find the solution to the system of...

Question 9

When writing the solution to the partial fraction decomposition of $\frac{x^{3}}{x^{2}-x-2}$ what is the first step of this solution?

Accepted Answer

A)  $\frac{x^{3}}{x^{2}-x-2}=\frac{A}{x-2}+\frac{B}{x+1}$ 
B)  $\frac{x^{3}}{x^{2}-x-2}=\frac{A x+B}{x-2}+\frac{C}{x+1}$ 
C)  $\frac{x^{3}}{x^{2}-x-2}=x+1+\frac{3 x+2}{x^{2}-x-2}$ 
D)  $\frac{x^{3}}{x^{2}-x-2}=x+\frac{3 x+2}{x^{2}-x-2}$ 
E)  $\frac{x^{3}}{x^{2}-x-2}=1+\frac{3 x+2}{x^{2}-x-2}$ 
A)  $\frac{x^{3}}{x^{2}-x-2}=\frac{A}{x-2}+\frac{B}{x+1}$ 
B)  $\frac{x^{3}}{x^{2}-x-2}=\frac{A x+B}{x-2}+\frac{C}{x+1}$ 
C)  $\frac{x^{3}}{x^{2}-x-2}=x+1+\frac{3 x+2}{x^{2}-x-2}$ 
D)  $\frac{x^{3}}{x^{2}-x-2}=x+\frac{3 x+2}{x^{2}-x-2}$ 
E)  $\frac{x^{3}}{x^{2}-x-2}=1+\frac{3 x+2}{x^{2}-x-2}$

Question 10

Write the system of equations for the augmented matrix. Do not solve.
$\left[\begin{array}{rrrr}
0 & 4 & 3 & -1 \
5 & 1 & -2 & 0 \
3 & 0 & 1 & 2
\end{array}\right]$

Accepted Answer

None

Solve the system graphically. Round answers to the nearest hundredth. y=4-7+3 y=-1+2x

Solve the system graphically. 8+32 =256 x =2y

Tell what elementary row operation can be applied to $\left[\begin{array}{rrrr}3 & 6 & -2 & 5 \\4 & 7 & 5 & -2 \\-3 & 2 & 0 & 3\end{array}\right]$ to obtain $\left[\begin{array}{rrrr}15 & 27 & 13 & -1 \\4 & 7 & 5 & -2 \\-3 & 2 & 0 & 3\end{array}\right]$

Find $A^{-1}$ of the matrix $A=\left[\begin{array}{rrr}1 & 0 & 0 \\-2 & 1 & 5 \\4 & 0 & 1\end{array}\right]$

Find the determinant of the matrix $B=\left[\begin{array}{rrr}2 & -1 & 4 \\3 & 1 & -2 \\1 / 2 & 4 & 5\end{array}\right]$ Does matrix B have an inverse?

Using matrix $A=\left[\begin{array}{rrr}3 & 7 & 4 \\2 & -1 & 6\end{array}\right]$ and $B=\left[\begin{array}{rrr}-1 & 5 & 2 \\7 & 10 & 1 \\-2 & 5 & -1\end{array}\right]$ which of the following is a true statement?

Solve the system by elimination. x-2y =4 x+y =1

Find the solution to the system of equations represented by the augmented matrix. $\left[\begin{array}{rrrr}1 & 3 & -4 & -13 \\0 & 1 & 2 & 4 \\0 & 0 & 1 & 3\end{array}\right]$

When writing the solution to the partial fraction decomposition of $\frac{x^{3}}{x^{2}-x-2}$ what is the first step of this solution?

Write the system of equations for the augmented matrix. Do not solve. $\left[\begin{array}{rrrr}0 & 4 & 3 & -1 \\5 & 1 & -2 & 0 \\3 & 0 & 1 & 2\end{array}\right]$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

Exam 7: Systems and Matrices

Solve the system graphically. Round answers to the nearest hundredth. y=4-7+3 y=-1+2x

Solve the system graphically. 8+32 =256 x =2y

Find A−1A^{-1}A−1 of the matrix A=[100−215401]A=\left[\begin{array}{rrr}1 & 0 & 0 \\-2 & 1 & 5 \\4 & 0 & 1\end{array}\right]A=​1−24​010​051​​

Find the determinant of the matrix B=[2−1431−21/245]B=\left[\begin{array}{rrr}2 & -1 & 4 \\3 & 1 & -2 \\1 / 2 & 4 & 5\end{array}\right]B=​231/2​−114​4−25​​ Does matrix B have an inverse?

Solve the system by elimination. x-2y =4 x+y =1

Find the solution to the system of equations represented by the augmented matrix. [13−4−1301240013]\left[\begin{array}{rrrr}1 & 3 & -4 & -13 \\0 & 1 & 2 & 4 \\0 & 0 & 1 & 3\end{array}\right]​100​310​−421​−1343​​

When writing the solution to the partial fraction decomposition of x3x2−x−2\frac{x^{3}}{x^{2}-x-2}x2−x−2x3​ what is the first step of this solution?

Write the system of equations for the augmented matrix. Do not solve. [043−151−203012]\left[\begin{array}{rrrr}0 & 4 & 3 & -1 \\5 & 1 & -2 & 0 \\3 & 0 & 1 & 2\end{array}\right]​053​410​3−21​−102​​

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

Find $A^{-1}$ of the matrix $A=\left[\begin{array}{rrr}1 & 0 & 0 \\-2 & 1 & 5 \\4 & 0 & 1\end{array}\right]$

Find the determinant of the matrix $B=\left[\begin{array}{rrr}2 & -1 & 4 \\3 & 1 & -2 \\1 / 2 & 4 & 5\end{array}\right]$ Does matrix B have an inverse?

Find the solution to the system of equations represented by the augmented matrix. $\left[\begin{array}{rrrr}1 & 3 & -4 & -13 \\0 & 1 & 2 & 4 \\0 & 0 & 1 & 3\end{array}\right]$

When writing the solution to the partial fraction decomposition of $\frac{x^{3}}{x^{2}-x-2}$ what is the first step of this solution?

Write the system of equations for the augmented matrix. Do not solve. $\left[\begin{array}{rrrr}0 & 4 & 3 & -1 \\5 & 1 & -2 & 0 \\3 & 0 & 1 & 2\end{array}\right]$