7. In R, the equation x1 + 2x2 + 3x3 defines a subspace U (a plane...

 

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7. In R³, the equation x1 + 2x2 + 3x3 defines a subspace U (a plane through the origin). Here (x1, x2, x3) = x € R³. a). Find a vector u € R³ such that U = {u}¹. As you know, such a vector u is called a normal vector of the plane. b). Find an orthonormal basis for U. = 0 7. In R³, the equation x1 + 2x2 + 3x3 defines a subspace U (a plane through the origin). Here (x1, x2, x3) = x € R³. a). Find a vector u € R³ such that U = {u}¹. As you know, such a vector u is called a normal vector of the plane. b). Find an orthonormal basis for U. = 0

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