Question

Write the matrix corresponding to the system of linear equations

2/3x-3y=4
y=-5

Answer 1

A X = Y
What is A?

Answer 2

\[

A= \left(
\begin{array}{cc}
\frac{2}{3} & -3 \\
0 & -5 \\
\end{array}
\right)

\]
is the matrix of coefficients
2/3 x -3 y
0 x -5 y

Answer 3

What is X?

Answer 4

what is X?

Answer 5

\[
X=
\left(
\begin{array}{c}
x \\
y \\
\end{array}
\right)

\]

Answer 6

\[

Y=\left(
\begin{array}{c}
4 \\
-5 \\
\end{array}
\right)
\]

Answer 7

Do you understand it?

Answer 8

\[
AX = \begin{pmatrix}
\frac{2}{3}x&+&-3y\\
0x&+&1y
\end{pmatrix}
\]

Answer 9

\[

\left(
\begin{array}{cc}
\frac{2}{3} & -3 \\
0 & -5 \\
\end{array}
\right)
\left(
\begin{array}{c}
x \\
y \\
\end{array}
\right)=\left(
\begin{array}{c}
4 \\
-5 \\
\end{array}
\right)
\]

Answer 10

My last post is the final answer

Answer 11

\[
AX = \begin{pmatrix}
\frac{2}{3}x&+&-3y\\
0x&+&1y
\end{pmatrix}
=
\begin{pmatrix}
\frac{2}{3}&-3\\
0&1
\end{pmatrix}
\begin{pmatrix}
x\\
y
\end{pmatrix}
\]

Answer 12

I guess this would be the most thorough way to show it:\[
AX =
\begin{pmatrix}
\frac{2}{3}x-3y\\
y
\end{pmatrix}
=
\begin{pmatrix}
\frac{2}{3}x&+&-3y\\
0x&+&1y
\end{pmatrix}
=
\begin{pmatrix}
\frac{2}{3}&-3\\
0&1
\end{pmatrix}
\begin{pmatrix}
x\\
y
\end{pmatrix}
\]And \(Y\) is very simple: \[
Y = \begin{pmatrix}
4\\
-5
\end{pmatrix}
\]