1.4.9 Represent a system of linear equations as a single matrix equation in a vector variable
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Subject
Mathematics
Date
Apr 3, 2024
Type
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Question and Solution Template
Learning Attribute(s) Included in Question
: 1.4.9 Represent a system of linear equations as a single matrix equation in a vector variable
.
Calculator Active?
No
Question
:
Represent following system of linear equations as a single matrix equation in a vector variable.
3
x
+
4
y
=
9
2
x
−
3
y
=
4
A)
(
3
2
4
−
3
)
(
x
y
)
=
(
4
9
)
B)
(
4
2
3
−
3
)
(
x
y
)
=
(
4
9
)
C)
(
3
4
2
−
3
)
(
x
y
)
=
(
9
4
)
D)
(
3
2
2
−
4
)
(
x
y
)
=
(
4
9
)
Correct answer: C
Equation Upload
(Please write the text of the question along with the LaTeX Code):
Represent following system of linear equations as a single matrix equation in a vector variable.
$3x+4y=9$
$2x-3y=4$
A) $\begin{pmatrix}3 & 2\\ 4&-3 \end{pmatrix} \begin{pmatrix}x\\
y \end{pmatrix}=\begin{pmatrix}4\\9 \end{pmatrix}$
B) $\begin{pmatrix}4 & 2\\ 3&-3 \end{pmatrix}\begin{pmatrix}x\\y \
end{pmatrix}=\begin{pmatrix}4\\9 \end{pmatrix}$
C) $\begin{pmatrix}3 & 4\\ 2&-3 \end{pmatrix}\begin{pmatrix}x\\y \
end{pmatrix}=\begin{pmatrix}9\\4 \end{pmatrix}$
D) $\begin{pmatrix}3 & 2\\ 2&-4 \end{pmatrix}\begin{pmatrix}x\\y \
end{pmatrix}=\begin{pmatrix}4\\9 \end{pmatrix}$
On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult):
6 i
Solution
:
Step 1
: The coefficient matrix for the above system is (
3
4
2
−
3
)
The variables are x
and y
. Write the variable matrix as (
x
y
)
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 1}:
The coefficient matrix for the above system is $\begin{pmatrix}3 & 4\\ 2&-3 \end{pmatrix}$
The variables are $x$ and $y$.
Write the variable matrix as $\begin{pmatrix}x\\y \end{pmatrix}$
Step 2:
On the right side of the equality the constant terms of the equations are 9
and 4
.
The matrix becomes (
9
4
)
Now, the system can be represented as (
3
4
2
−
3
)
(
x
y
)
=
(
9
4
)
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 2}: On the right side of the equality the constant terms of the equations are $9$ and $4$.
The matrix becomes $\begin{pmatrix}9\\4 \end{pmatrix}$
Now, the system can be represented as $$\begin{pmatrix}3 & 4\\ 2&-
3 \end{pmatrix}\begin{pmatrix}x\\y \end{pmatrix}=\begin{pmatrix}9\\4
\end{pmatrix}$$
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