taiwan-gsat 2007 Q8

taiwan-gsat · Other · gsat__math Matrices Linear System and Inverse Existence
8. Which of the following matrices can be transformed into $\left(\begin{array}{llll} 1 & 2 & 3 & 7 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 1 & 1 \end{array}\right)$ through a series of row operations?
(1) $\left(\begin{array}{llll} 1 & 2 & 3 & 7 \\ 0 & 1 & 1 & 2 \\ 0 & 2 & 3 & 5 \end{array}\right)$
(2) $\left(\begin{array}{cccc} -1 & 3 & -1 & 0 \\ -1 & 1 & 1 & 0 \\ 3 & 1 & -7 & 0 \end{array}\right)$
(3) $\left(\begin{array}{cccc} 1 & 1 & 2 & 5 \\ 1 & -1 & 1 & 2 \\ 1 & 1 & 2 & 5 \end{array}\right)$
(4) $\left(\begin{array}{cccc} 2 & 1 & 3 & 6 \\ -1 & 1 & 1 & 0 \\ -2 & 2 & 2 & 1 \end{array}\right)$
(5) $\left(\begin{array}{llll} 1 & 3 & 2 & 7 \\ 0 & 1 & 1 & 2 \\ 0 & 1 & 0 & 1 \end{array}\right)$
& 1,5 & & 19 & 9 & & 39 & 2
8. Which of the following matrices can be transformed into $\left(\begin{array}{llll} 1 & 2 & 3 & 7 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 1 & 1 \end{array}\right)$ through a series of row operations?\\
(1) $\left(\begin{array}{llll} 1 & 2 & 3 & 7 \\ 0 & 1 & 1 & 2 \\ 0 & 2 & 3 & 5 \end{array}\right)$\\
(2) $\left(\begin{array}{cccc} -1 & 3 & -1 & 0 \\ -1 & 1 & 1 & 0 \\ 3 & 1 & -7 & 0 \end{array}\right)$\\
(3) $\left(\begin{array}{cccc} 1 & 1 & 2 & 5 \\ 1 & -1 & 1 & 2 \\ 1 & 1 & 2 & 5 \end{array}\right)$\\
(4) $\left(\begin{array}{cccc} 2 & 1 & 3 & 6 \\ -1 & 1 & 1 & 0 \\ -2 & 2 & 2 & 1 \end{array}\right)$\\
(5) $\left(\begin{array}{llll} 1 & 3 & 2 & 7 \\ 0 & 1 & 1 & 2 \\ 0 & 1 & 0 & 1 \end{array}\right)$