98年國立中央大學資工所線性代數線上測驗

年度

年度

1.: Every n × n matrix has n eigenvalues and n eigenvectors

2.: Similar matrices have the same
(A): (a) solution set
(B): (b) general structure
(C): (c) eigenvalues
(D): (d) eigenvectors.

3.: If A is row equivalent to the identity matrix I, then A is diagonalizable.

4.: If A is a square matrix with orthonormal columns, then A is invertible

5.

6.
(A): (a) rank = 2, nullity = 2,
(B): (b) rank = 3, nullity = 1,
(C): (c) rank = 2, nullity = 4,
(D): (d) rank = 1, nullity = 3.

7.: Let A be an m × n matrices, P be an invertible m × m matrix, and Q be an n × n matrix.
Which of the following statements are true?
(A): (a) rank(AQ) = nullity(A),
(B): (b) rank(AQ) = rank(A),
(C): (c) rank(PA) = rank(P)
(D): (d) rank(PA) = rank(A).

8.: If A is an n × n symmetric matrix, then
(A): (a) A is always diagonalizable.
(B): (b) A is orthogonally diagonalizable
(C): (c) A has nonnegative eigenvalues
(D): (d) A always has n linearly independent eigenvectors
(E)

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