题目23. 设\(A_{m\times n}V_{n\times r}=U_{m\times r}\Sigma_{r\times r}\),则下述四个基本子空间的关系,哪个是正确的: A: \(\mathbb{R}^n=C(A^T)\oplus N(A)\) B: \(\mathbb{R}^m=C(A^T)\oplus N(A)\) C: \(\mathbb{R}^n=C(A^TA)\oplus N(AA^T)\) D: \(\mathbb{R}^m=C(A^TA)\oplus N(AA^T)\)
题目23. 设\(A_{m\times n}V_{n\times r}=U_{m\times r}\Sigma_{r\times r}\),则下述四个基本子空间的关系,哪个是正确的: A: \(\mathbb{R}^n=C(A^T)\oplus N(A)\) B: \(\mathbb{R}^m=C(A^T)\oplus N(A)\) C: \(\mathbb{R}^n=C(A^TA)\oplus N(AA^T)\) D: \(\mathbb{R}^m=C(A^TA)\oplus N(AA^T)\)
题目24. 设线性空间\(V\)的线性变换\(\sigma\)满足\(\sigma^2=\sigma\),则称\(\sigma\)为投影(projection)。以下说法错误的是: A: \(V\)中向量\(\beta\in Im\sigma\)当且仅当<br/>\(\sigma\beta=\beta\) B: \(V=Im\sigma+ker\sigma\) C: \(Im\sigma\cap ker\sigma\neq\{0\}\) D: \(V=Im\sigma\oplus ker\sigma\)
题目24. 设线性空间\(V\)的线性变换\(\sigma\)满足\(\sigma^2=\sigma\),则称\(\sigma\)为投影(projection)。以下说法错误的是: A: \(V\)中向量\(\beta\in Im\sigma\)当且仅当<br/>\(\sigma\beta=\beta\) B: \(V=Im\sigma+ker\sigma\) C: \(Im\sigma\cap ker\sigma\neq\{0\}\) D: \(V=Im\sigma\oplus ker\sigma\)
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