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Chapter 2: Q42E (page 74)

Let T(x鈫�)=projL(x鈫�)be the orthogonal projection onto a line in鈩�2 . What is the relationship between T(x鈫�)andT(T(x鈫�))? justify your answer carefully.

Short Answer

Expert verified

T(x鈫�)=T(T(x鈫�)),is the relation between T(x鈫�) and .T(T(x鈫�))

Step by step solution

01

Compute the linear transformation. 

The relation between the linear transformation and the projection is,

T(x鈫�)=projL(x鈫�)

The above equation represents the linear transformation of the vector x鈬赌onto the lineL.

The transformation of the matrix of the form is called a linear transformation.

The linear transformation is only the transformation and neither reflection nor rotation.

02

Define the relation 

The linear transformation is represented as, .T(x鈫�)

The transformation of the linear transformation is represented as,T(T(x鈫�)) .

Thus, the relation between these two is, .T(x鈫�)=T(T(x鈫�))

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