设A为[tex=2.714x1.071]319e/AVA5VexfWBQXpJ9ug==[/tex]矩阵，证明矩阵方程[tex=3.643x1.214]+a3DWsDTkgfLfEl0RHCLyw==[/tex]有解的充分必要条件是[tex=4.357x1.357]jEEivN/5gJOW4N32rCGoUCD/BSCzPVhNAj+HIfDhvis=[/tex]

设有齐次线性方程组[tex=2.929x1.0]qTT9ohZSoF+wT3IvQFgnLBHrLWFsrmsJaVbb7qafUBgAyALM4mNdkhoHjzQgql/8[/tex]和[tex=2.929x1.0]d3oLifbI5s6LUr2fYOYYY1ttPIjl5chscg3/Vox7gwzi+iuyxK7t/MB7PQpYYKyA[/tex]，其中[tex=0.857x1.286]VDaqe/5gsI6W8PDnV4Qzpg==[/tex]，[tex=0.786x1.286]7xu/f2QGSkxbr3vOcRhylg==[/tex]均为[tex=2.714x1.071]319e/AVA5VexfWBQXpJ9ug==[/tex]矩阵，现有四个命题：①若[tex=2.929x1.0]qTT9ohZSoF+wT3IvQFgnLBHrLWFsrmsJaVbb7qafUBgAyALM4mNdkhoHjzQgql/8[/tex]的解均是[tex=2.929x1.0]d3oLifbI5s6LUr2fYOYYY1ttPIjl5chscg3/Vox7gwzi+iuyxK7t/MB7PQpYYKyA[/tex]的解，则[tex=5.643x1.357]jEEivN/5gJOW4N32rCGoUF7XeM+ib9DUenO1ibV2ayHh86BnqfIhZX01v1n343Bj[/tex]；②若[tex=5.643x1.357]jEEivN/5gJOW4N32rCGoUF7XeM+ib9DUenO1ibV2ayHh86BnqfIhZX01v1n343Bj[/tex]，则[tex=2.929x1.0]qTT9ohZSoF+wT3IvQFgnLBHrLWFsrmsJaVbb7qafUBgAyALM4mNdkhoHjzQgql/8[/tex]的解均是[tex=2.929x1.0]d3oLifbI5s6LUr2fYOYYY1ttPIjl5chscg3/Vox7gwzi+iuyxK7t/MB7PQpYYKyA[/tex]的解；③若[tex=2.929x1.0]qTT9ohZSoF+wT3IvQFgnLBHrLWFsrmsJaVbb7qafUBgAyALM4mNdkhoHjzQgql/8[/tex]与[tex=2.929x1.0]d3oLifbI5s6LUr2fYOYYY1ttPIjl5chscg3/Vox7gwzi+iuyxK7t/MB7PQpYYKyA[/tex]同解，则[tex=5.643x1.357]jEEivN/5gJOW4N32rCGoUPa2P8TiVo92+43RL9tve5cuxdTnqaCD3yUNjKmBJXCx[/tex]；④若[tex=5.643x1.357]jEEivN/5gJOW4N32rCGoUPa2P8TiVo92+43RL9tve5cuxdTnqaCD3yUNjKmBJXCx[/tex]，则[tex=2.929x1.0]qTT9ohZSoF+wT3IvQFgnLBHrLWFsrmsJaVbb7qafUBgAyALM4mNdkhoHjzQgql/8[/tex]与[tex=2.929x1.0]d3oLifbI5s6LUr2fYOYYY1ttPIjl5chscg3/Vox7gwzi+iuyxK7t/MB7PQpYYKyA[/tex]同解。以上命题中正确的是  未知类型：{'label': 'questionDesc', 'content': '[tex=3.286x1.357]akNi1EvuYp8tNA+5BL4rmD22VMBSPXvRce9MxfeYUng=[/tex]', 'isMemberControl': 0, 'type': 181} A: ①② B: ①③ C: ②④ D: ③④

设[tex=2.714x1.071]319e/AVA5VexfWBQXpJ9ug==[/tex]矩阵S=A的秩[tex=6.0x1.357]jEEivN/5gJOW4N32rCGoULk3zJgyT4ZeUva2EruKMvk=[/tex]，则 未知类型：{'options': ['A的任意m个列向量所成向量组线性无关', 'A的任意一个m阶子式不为零', '若[tex=3.071x1.0]SA/CYYfbcBgMcSrKlwD1tQ==[/tex]，则[tex=2.357x1.0]+LH2F83OwYsc3Vu3YAj4ng==[/tex]', '通过矩阵的初等行变换，必可化为[tex=3.357x1.357]x+7oUtbux4t2Tm8+oBz57fbFCT66PMNcZxM9UFfTqjI=[/tex]的形式'], 'type': 102}