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Chapter 4: Q40E (page 177)

Ifc鈫� is any vector in Rn, what are the possible dimensions of the space V of alln脳n matrices A such that Ac鈫�=0鈫�?

Short Answer

Expert verified

The solution is 0,n,2nor3n.

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

Explanation for the solution of the possible dimensions of the space V

Consider ac鈫� is any vector inRn and also assume thatAc鈫�=0鈫�

Here, then脳n matrix of A becomes

When apply the位滨-A in the diagonal matrix of thec鈫� vector, then the value of eigenvector are 0,n,2nor3n.

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