中文摘要：

该文讨论了几何直观在线性代数教学中的重要性,对几个较为抽象的代数观念如：线性相关、线性无关、行列式、直和等以及一些常用代数方法如：斯密特正交化、最小二乘法等总结出了它们在二维或三维欧氏几何中的相应解释,结合几个例子说明了代数与几何之间的紧密联系,说明了在线性代数教学中贯彻数形结合思想的重要性。

英文摘要：

this paper discusses about the importance of geometric intuition in linear algebra.First,we provide the 2--dimension/3--dimension euclidean geometric meaning of several abstract algebraic concepts, such as linearly dependence,linearly independence, determinant and direct sum.Further,we provide the 2--dimension/3--dimension euclidean geometric meaning of some common algebraic methods, Such as schmidt orthogonalization and least square method.By some illustrative examples,we finally show the relationship between algebra and geometry and point out the importance of symbolic--graphic combination in education of linear algebra.