The matrix representation of a linear transformation T with respect to a basis B is given by the images of the basis vectors under T. In this case, the basis B={v1,v2,v3,v4} and the images of the basis vectors under T are T(v1)=v2, T(v2)=v3, T(v3)=v4, and T(v4)=v1.

We can represent these transformations as columns in a matrix. The matrix M representing T with respect to B is:

M = [0 0 0 1
1 0 0 0
0 1 0 0
0 0 1 0]

This matrix is not symmetric (it is not equal to its transpose), not orthogonal (its columns are not orthonormal), and not the identity matrix (it does not have ones on the diagonal and zeros elsewhere).

However, it is a singular matrix because its determinant is zero. Therefore, the correct answer is C. singular.

Question

The matrix representation of a linear transformation T with respect to a basis B is given by the images of the basis vectors under T. In this case, the basis B={v1,v2,v3,v4} and the images of the basis vectors under T are T(v1)=v2, T(v2)=v3, T(v3)=v4, and T(v4)=v1.

We can represent these transformations as columns in a matrix. The matrix M representing T with respect to B is:

M = [0 0 0 1
     1 0 0 0
     0 1 0 0
     0 0 1 0]

This matrix is not symmetric (it is not equal to its transpose), not orthogonal (its columns are not orthonormal), and not the identity matrix (it does not have ones on the diagonal and zeros elsewhere).

However, it is a singular matrix because its determinant is zero. Therefore, the correct answer is C. singular.

Knowee AI · Accepted Answer

The matrix representation of a linear transformation T with respect to a basis B is given by the images of the basis vectors under T. In this case, the basis B={v1,v2,v3,v4} and the images of the basis vectors under T are T(v1)=v2, T(v2)=v3, T(v3)=v4, and T(v4)=v1.

We can represent these transformations as columns in a matrix. The matrix M representing T with respect to B is:

M = [0 0 0 1
     1 0 0 0
     0 1 0 0
     0 0 1 0]

This matrix is not symmetric (it is not equal to its transpose), not orthogonal (its columns are not orthonormal), and not the identity matrix (it does not have ones on the diagonal and zeros elsewhere).

However, it is a singular matrix because its determinant is zero. Therefore, the correct answer is C. singular.

Let B={v1,v2,v3,v4} be a basis for a vector space V. Then the matrix with respect to B for the linear operator T:V→V defined by T(v1)=v2,T(v2)=v3,T(v3)=v4,T(v4)=v1 isA. symmetric matrixB. orthogonal matrixC. singularD. identity matrix

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