这是一道线性代数题.求一组R^4空间的正交基,第一个基向量与u平行.In the space R^4 form an orthogonal basis such that the first basis vector is parallel to the vector u=(0,-3,0,4).
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![这是一道线性代数题.求一组R^4空间的正交基,第一个基向量与u平行.In the space R^4 form an orthogonal basis such that the first basis vector is parallel to the vector u=(0,-3,0,4).](/uploads/image/z/8812121-41-1.jpg?t=%E8%BF%99%E6%98%AF%E4%B8%80%E9%81%93%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E9%A2%98.%E6%B1%82%E4%B8%80%E7%BB%84R%5E4%E7%A9%BA%E9%97%B4%E7%9A%84%E6%AD%A3%E4%BA%A4%E5%9F%BA%2C%E7%AC%AC%E4%B8%80%E4%B8%AA%E5%9F%BA%E5%90%91%E9%87%8F%E4%B8%8Eu%E5%B9%B3%E8%A1%8C.In+the+space+R%5E4+form+an+orthogonal+basis+such+that+the+first+basis+vector+is+parallel+to+the+vector+u%3D%280%2C-3%2C0%2C4%29.)
这是一道线性代数题.求一组R^4空间的正交基,第一个基向量与u平行.In the space R^4 form an orthogonal basis such that the first basis vector is parallel to the vector u=(0,-3,0,4).
这是一道线性代数题.求一组R^4空间的正交基,第一个基向量与u平行.
In the space R^4 form an orthogonal basis such that the first basis vector is parallel to the vector u=(0,-3,0,4).
这是一道线性代数题.求一组R^4空间的正交基,第一个基向量与u平行.In the space R^4 form an orthogonal basis such that the first basis vector is parallel to the vector u=(0,-3,0,4).
这样的解很多的,下面我构造(注意是造)其中一组R^4空间的单位正交向量组.
e1,we have known e1//u;
we let e2=(0,4,0,3),and it content (e1⊥e2)
then,let e3=(1,0,1,0),it content (e3⊥e1,e3⊥e2)
At last,let e4=(-1,0,1,0),e4 content (e4⊥e1,e4⊥e2,e4⊥e3)
And then,get them to be basis vector
e1=(0,-3/√5,0,4/√5)
e2=(0,4/√5,0,3/√5)
e3=(1/√2,0,1/√2,0)
e4=(-1/√2,0,1/√2,0)
This is only one solution and or course,there are other solutions .
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