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Chapter 4: Q44E (page 177)

If matrix A represents the orthogonal projection onto a plane in R3 ,what is the dimension of the space V of all matrices S such thatAS=S(100010000)?See Exercise 43.

Short Answer

Expert verified

The dimensions of the space V of all 3脳3 matrices S is3 .

Step by step solution

01

Explanation for the dimension of the space

If a linear space has a basis with n elements then all other bases of V, consists of n elements as well.

Also we say that n is the dimension of V

dim(V)=n

02

 Step 2:Solution for the dimension of the space V

Consider the matrix A which represents the orthogonal projection about a plane V inR3

HereAS=S(100010000)is the matrix of the orthogonal projection about a plane V

Here A is the3脳3matrix of the orthogonal projection about the plane V.

Thus,n=3in the matrices S of the orthogonal projection about the plane V.

dim(V)=ndim(V)=3

Since the solution.

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