设[tex=4.429x1.214]W1uTpzbbehOOliAP2ns4cw==[/tex]为[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]阶矩阵，且[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]可逆，[tex=3.714x1.0]MAuhFkvlOKAcUPNAmJx/oQ==[/tex]，证明[tex=9.643x2.786]Uyz5s0rmQIddjb5Jc2T/YRd9exX63872DgLG3it+eRA4jyxpzsJs9AO2ePRWjqmQFpWcrISvmUMO1aYjcaW3M/ZuDdes+o1ZXeyF+wyNlPU=[/tex] .
举一反三
- 设[tex=4.429x1.214]W1uTpzbbehOOliAP2ns4cw==[/tex]都是[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex] 阶方阵，且[tex=3.714x1.0]MAuhFkvlOKAcUPNAmJx/oQ==[/tex]，证明：[tex=9.643x2.786]Uyz5s0rmQIddjb5Jc2T/YSwnwxLJ9Z0Yd88BZD2//sramD6rSrLmaXcDSI7d7lwkOk2AYXOCq2cjVdbU4QyEjRDtLJaybbZwv8oG6Cr9V4g=[/tex] (1)
- 设[tex=4.429x1.214]jR8POt5zCPHNh36sbaTE/A==[/tex]都是数域[tex=0.857x1.0]eMszuSG5by5UfRZVROYp5A==[/tex]上的[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]级矩阵，且[tex=3.714x1.0]sFM5phea1FPTO6duvP4I7w==[/tex].证明：[tex=9.643x2.786]Uyz5s0rmQIddjb5Jc2T/YSwnwxLJ9Z0Yd88BZD2//sramD6rSrLmaXcDSI7d7lwkOk2AYXOCq2cjVdbU4QyEjRDtLJaybbZwv8oG6Cr9V4g=[/tex].
- 已知[tex=1.786x1.214]IENxQEh5u4RdnCaqHm72Xg==[/tex]为3阶矩阵，且[tex=6.5x1.357]Xw38Dcvrbs7IEKOZRvkd5g==[/tex]，其中[tex=0.786x1.0]XvHgf70VtK2FH5G93l0k3g==[/tex]是3阶单位矩阵．(1)证明：矩阵[tex=2.786x1.143]RcZ2ZRIlzxNTbD8lUHAX+Q==[/tex]可逆；(2)若[tex=7.786x3.5]DgXZT9CtCPAglTYwc4pEdVwGPrEvfplbNSz07f1CHm3lKZFzRkIi88nqRWCa7cdxtDn1Uq6Au4bDH+3NSK9+pGWuIrunnKgMXUiXxap7tYqS5e4P0ZLrWW76zZyDl/um[/tex]，求矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]
- 设 [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 为 [tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex] 阶实矩阵, 满足 [tex=3.643x1.214]u9ZFFjrmdLitRdLiKCtqhjog7ZeYbiv+qENyuyHI7/w=[/tex], 求证: [tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex] 是对称矩阵.
- 设3阶矩阵[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]的特征值为-2, -1, 3,矩阵[tex=6.786x1.357]5sQBSCH1+oEoQda8DcapHw==[/tex],求矩阵[tex=0.786x1.0]ri6gmnf1+J9dGqG5/1sV6A==[/tex]的行列式[tex=1.357x1.357]JRr5OoiiAPF9KB2ukKJtuw==[/tex]