Matrices

When one of the eigen values of the matrix A is 0, then the determinant of A is _____.

• 0

• 1

• -1

• 2

When the eigen values of a matrix are 0,1,2, the matrix A is said to be

• Non singular matrix

• unit matrix

• singular matrix

• None of these

The product of eigen values of a matrix is equal to the ____ of the matrix

• sum of diagonal elements

• Determinant

• sum of all elements

• eigen vectors

If all the eigen values are positive then the nature of the quadratic form is ___

• Positive definite

• Negative definite

• Indefinite

• Positive semidefinite

• 1 and 25    

• 6 and 4

• 2 and 3

• 1 and 125

__________ eigenvector is found out by dividing each element by magnitude of column vector.

• Normalized

• Model

• signature

• index

A homogeneous polynomial of the second degree in any number of variables is called a__.

• ssignature

• index

• rank

• quadratic form

The number of positive square terms in the canonical form is called the ___ of the quadratic form.

• signature

• index

• rank

• quadratic form

1.               A square matrix A and its transpose have the ____ Eigen values.

• distinct

• same

• zero

• unit

The difference of number of positive and negative square terms =
𝑠 – (𝑟 – 𝑠) = 2𝑠 – 𝑟 is called the _____ of the quadratic form.

• index

• rank

• signature

• indefinite