解 将增广矩阵化成行最简形<br/><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/160801393748498bf406c87a848829203b21488a2027dimage55.png"style="width:436px;height:75px;"/>(6分)<br/>原方程组有解. (8分)<br/><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/160801393751722ac794ecbe348e1b409db97933b9077image56.png"style="width:121px;height:51px;"/>.<br/>令<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1608013937551c95dc25965b44b058d3bb0849f848e05image57.png"style="width:73px;height:51px;"/>,得到原方程的一个解<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/16080139376021b059953c6f244f998720201d09617a2image58.png"style="width:27px;height:17px;"/><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1608013937637ef3b02fb040d4b3d948af9a236093122image59.png"style="width:28px;height:96px;"/>. (10分)<br/>原方程对应的齐线性方程组同解于<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1608013937667cc1ae3d7cc244d11bab39fcc58e7f8ebimage60.png"style="width:85px;height:51px;"/>,<br/>令<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1608013937704297daea9df224b4aba3a0ce02ed4bca7image61.png"style="width:101px;height:51px;"/>,则求得对应齐次方程组的基础解系为:<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/16080139377391dd0d8b8185043ed8a9eefe995a1ad03image62.png"style="width:116px;height:96px;"/>.(12分)<br/>故所求原方程的解为<img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1608013937775e72100daab1d4da5b69dc25a897080e5image63.png"style="width:35px;height:99px;"/><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/160801393780809cdf3cf75e4460a9268db9708971e7cimage64.png"style="width:104px;height:96px;"/><img src="https://s3.cn-north-1.amazonaws.com.cn/qingshuxuetang/examination/imgUplod/1608013937844135dc36cfd4d4994bc62601f1421c424image65.png"style="width:40px;height:96px;"/>. K1,k2为任意常数. (15分)
解 将增广矩阵化成行最简形(6分)原方程组有解. (8分).令,得到原方程的一个解. (10分)原方程对应的齐线性方程组同解于,令,则求得对应齐次方程组的基础解系为:.(12分)故所求原方程的解为. K1,k2为任意常数. (15分)