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Question

  is a square matrix. Select all statement(s) from below choices that are NOT correct.

a.) If  then has only one solution for any 

b.) If  is an eigenvalue of  then we can always find two different corresponding eigenvectors which are not multiple of each other.

c.) If then  has an inverse.

d.) If is an eigenvalue of , then we can always find two different corresponding eigenvectors which are multiple of each other.

Answer 1

(a). TRUE If l D l is nonzero, then D^-1 exists. So, Dx = b has the unique solution x = D^-1b.

Note that if D is n x n, then x and b are n x 1 column vectors.

(c). FALSE If l D l = 0, then D is not invertible.

(b) FALSE If v is an eigenvector corresponding to λ, then so is kv (k ≠ 0).

(d) TRUE See part (b).

Answer 2

If the determinant is zero, you cannot invert the matrix