A: \( r\left( B \right) < k \)
B: \( r\left( B \right) = k \)
C: \( r\left( B \right) \ge k \)
D: \( r\left( B \right) \le k \)
举一反三
- 设 \( A \)是 \( n \)阶方阵,\( R\left( A \right) = r < n \) ,那么( ) A: \( A \)可逆 B: \( A \)中所有\( r \) 阶子式不为零 C: \( \left| A \right| = 0 \) D: \( A \) 中没有不等于零的\( r \)阶子式
- 1.设${{J}_{k}}=\int_{{}}^{{}}{\frac{dx}{{{\left[ {{(x+a)}^{2}}+{{b}^{2}} \right]}^{k}}}}\quad (b\ne 0)$,则${{J}_{k}}$满足( )。 A: ${{J}_{k+1}}=\frac{1}{2k{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}-(2k-1){{J}_{k}} \right],\quad (k\ge 2)$ B: ${{J}_{k+1}}=\frac{1}{2k{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}+(2k-1){{J}_{k}} \right],\quad (k\ge 2)$ C: ${{J}_{k+1}}=\frac{1}{2{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}+(2k+1){{J}_{k}} \right],\quad (k\ge 2)$ D: ${{J}_{k+1}}=\frac{1}{2{{b}^{2}}}\left[ (x+a){{\left( {{(x+a)}^{2}}+{{b}^{2}} \right)}^{-k}}+(2k-1){{J}_{k}} \right],\quad (k\ge 2)$
- \(A,B\)均为\(n\)阶方阵,且\(A\)与\(B\)合同,\( R\left( A \right) = 4 \),则\( R\left( B \right) = \) ______
- 若幂级数\(\sum\limits_{n = 1}^\infty { { a_n}} {x^n}\)在\(x = {x_0}\)处发散,则该级数的收敛半径满足( )。 A: \(R = \left| { { x_0}} \right|\) B: \(R < \left| { { x_0}} \right|\) C: \(R > \left| { { x_0}} \right|\) D: \(R \le \left| { { x_0}} \right|\)
- 设\( A \)是\( n \)阶方阵,\( R(A) = r < n \),那么( ) A: \( A \)可逆 B: \( A \)中所有\( r \)阶子式全不为零 C: \( \left| A \right| = 0 \) D: \( A \)中没有不等于零的\( r \)阶子式
内容
- 0
设`\n`阶方阵`\A`经过初等变换后得方阵`\B`,则 ( ) A: \[\left| {\rm{A}} \right| = \left| {\rm{B}} \right|\] B: \[\left| A \right| \ne \left| B \right|\] C: \[\left| A \right|\left| B \right| \ge {\rm{0}}\] D: 若`\| A| = 0`,则`\| B| = 0`
- 1
设\( A,B \)均为\( n \)阶方阵,则必有( ) A: \( \left| {A + B} \right| = \left| A \right| + \left| B \right| \) B: \( AB = BA \) C: \( \left| {AB} \right| = \left| {BA} \right| \) D: \( {\left( {A + B} \right)^{ - 1}} = {A^{ - 1}} + {B^{ - 1}} \)
- 2
设\( A,B \) 为方阵,则 \( \left| {AB} \right| = \,\left| A \right|\,\left| B \right| \)。( )
- 3
设\( n \) 阶方阵 \( A,B \)相似,则 \( \left| A \right| = \left| B \right| \).
- 4
设\( A,\;B \) 均为\( n \) 阶方阵,则必有( ). A: \( {(A + B)^2} = {A^2} + 2AB + {B^2} \) B: \( \left| {A + B} \right| = \left| A \right| + \left| B \right| \) C: \( \left| {AB} \right| = \left| A \right|{\kern 1pt} \left| B \right| \) D: \( {\left( {AB} \right)^{\rm T}} = {A^{\rm T}}{B^{\rm T}} \)