Linear Algebra-2

If x is an Eigen vector for matrix A then Ax and x will have relationship

• Ax is perpendicular to x

• Ax is parallel to x

• Data is insufficient

What are the Eigen vectors with eigen values Zero?

• They are the one in RowSpace

• They are the one in NullSpace

• They are the one in ColumnSpace

If the trace of a 3x3 matrix is 10 and two of its Eigen Values are 5 and 3, then the remaining Eigen value will be

• 8

• 10

• 2

• 3

• Matrix A should be singular

• (-2,4)

• (2,-4)

• (2,4)

• (-2,-4)

• (1, -1)

  (-1, 1)

• (1, 1)

  (-1, 1)

• (1, 0)

  (-1, 1)

• (1, 1)

  (-1, 0)

Diagonalization of a matrix will not be possible if

• The matrix is degenerate

• The matrix is symmetric

• The eigen values are repeated

• If the matrix is triangular

If the matrix is Sque-symmetric then the eigen values will be:

• Real and distinct

• Real and equal

• Imaginary and complex conjugate

• Imaginary and equal

If C is a Cofactor matirx of A then the inverse of A can be written as

For the matrix in question the determinant will be:

• 1

• 2

• 3

• 4