作业帮线性代数关于矩阵的问题、
来源：学生作业帮 编辑：作业帮 分类：英语作业 时间：2024/05/14 19:33:57
线性代数关于矩阵的问题、
Suppose that AX = B is the matrix representation of a system of linear
equations.
(a) Suppose that Y is a solution of this system,and that Z1 and Z2 are solutions of
the associated homogeneous system.Show that Y 17Z1 + 16Z2 is also a solution of
AX = B .
(b) Suppose that Y1 and Y2 are solutions of AX = B .Show that 2Y1 Y2 is also a
solution of AX = B .
Suppose that AX = B is the matrix representation of a system of linear
equations.
(a) Suppose that Y is a solution of this system,and that Z1 and Z2 are solutions of
the associated homogeneous system.Show that Y 17Z1 + 16Z2 is also a solution of
AX = B .
(b) Suppose that Y1 and Y2 are solutions of AX = B .Show that 2Y1 Y2 is also a
solution of AX = B .
it's easy to see that if Z1 and Z2 is the solutions of the linear system,then any combination of them is also the solution according to the definition of linear.you can do a little opearor such as :
AY1=B,AY2=B,so A(2Y1-Y2)=2AY1-AY2=2B-B=B...OK get the result~
再问： 第一题的步骤能再完整一点么,我基本能看懂,但需要详细的步骤去证明那个式子is also a solution
再答： (a) is similar to (b), where (17Z1-16Z2) works as (2Y1-Y2). detail is express as following: A(Y)=A(17Z1-16Z2)=17AZ1-16AZ2=17B-16B=B, well, you should find rule during this kind of questions~ My honour to anwer your problems
AY1=B,AY2=B,so A(2Y1-Y2)=2AY1-AY2=2B-B=B...OK get the result~
再问： 第一题的步骤能再完整一点么,我基本能看懂,但需要详细的步骤去证明那个式子is also a solution
再答： (a) is similar to (b), where (17Z1-16Z2) works as (2Y1-Y2). detail is express as following: A(Y)=A(17Z1-16Z2)=17AZ1-16AZ2=17B-16B=B, well, you should find rule during this kind of questions~ My honour to anwer your problems