Aliza J.

asked • 08/20/20

Linear systems that have infinite many solutions.

From below choices, select all linear systems that have LaTeX: \infty many solutions.

A.)LaTeX: \left[\begin{array}{rrrr}
1&0&0&0\\
2&3&0&0\\
4&5&6&0\\
7&8&9&10
\end{array}\right]
\cdot
\left[\begin{array}{c}
y_1\\
y_2\\
y_3\\
y_4
\end{array}\right]
=
\left[\begin{array}{r}
-3\\
7\\
4\\
11\end{array}\right]

B.) LaTeX: \left[\begin{array}{rrrr}
1&0&0&1\\
0&1&1&0\\
0&0&0&0
\end{array}\right]
\cdot
\left[\begin{array}{c}
y_1\\
y_2\\
y_3\\
y_4
\end{array}\right]
=
\left[\begin{array}{r}
2\\
3\\
-5\end{array}\right]

C.) LaTeX: \left[\begin{array}{rrrr}
0&1&0&0\\
0&0&1&0\\
0&0&0&1
\end{array}\right]
\cdot
\left[\begin{array}{c}
y_1\\
y_2\\
y_3\\
y_4
\end{array}\right]
=
\left[\begin{array}{r}
0\\
0\\
0\end{array}\right]

D.) LaTeX: \left[\begin{array}{rrrr}
1&1&1&1\\
3&3&3&3\\
4&4&4&4
\end{array}\right]
\cdot
\left[\begin{array}{c}
y_1\\
y_2\\
y_3\\
y_4
\end{array}\right]
=
\left[\begin{array}{r}
1\\
3\\
4\end{array}\right]

E.) LaTeX: \left[\begin{array}{rrrr}
1&0&1&0\\
0&0&0&0\\
0&1&0&1
\end{array}\right]
\cdot
\left[\begin{array}{c}
y_1\\
y_2\\
y_3\\
y_4
\end{array}\right]
=
\left[\begin{array}{r}
2\\
0\\
-2\end{array}\right]

F.) LaTeX: \left[\begin{array}{rrrr}
1&1&1&1
\end{array}\right]\cdot
\left[\begin{array}{c}
y_1\\
y_2\\
y_3\\
y_4\end{array}\right]
= 0

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