Question

求大神指点，并写出步骤

Answer 1

挑战下,五阶方阵用行变换方式,化为这样会不会看到头晕呢?(A,E)=|c000010000||1c00001000|、这行乘以c,减去第一行|01c0000100||001c000010||0001c00001|=|c000010000||0c²000-1c000||01c0000100|、这行乘以c²,减去第二行|001c000010||0001c00001|=|c000010000||0c²000-1c000||00c³001-cc²00||001c000010|、这行乘以c³,减去第三行|0001c00001|=|c000010000||0c²000-1c000||00c³001-cc²00||000c⁴0-1c-c²c³0||0001c00001|、这行乘以c⁴,减去第四行=|c000010000|、这行除以c|0c²000-1c000|、这行除以c²|00c³001-cc²00|、这行除以c³|000c⁴0-1c-c²c³0|、这行除以c⁴|0000c⁵1-cc²-c³c⁴|、这行除以c⁵=|100001/c0000||01000-1/c²1/c000||001001/c³-1/c²1/c00||00010-1/c⁴1/c³-1/c²1/c0||000011/c⁵-1/c⁴1/c³-1/c²1/c|所以A的逆矩阵A⁻¹=|1/c0000||-1/c²1/c000||1/c³-1/c²1/c00||-1/c⁴1/c³-1/c²1/c0||1/c⁵-1/c⁴1/c³-1/c²1/c|