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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