Matrix and Vector Space Quiz

Which of the following is empty set?

• b) ∅

• c) ∅

• d) all of them

Rank of matrix A = 2332483612 is

• b) 0

• c) 2

• d) 3

T: V→W is a linear transformation if T(u + v) = T(u) +T(v) T(ku) = kT(u)

• (a) and (b) both

• None

A square matrix A = aij is skew- Hermitian if

• A = AT

• b) A = -AT

• c) AT = A

• d) AT = - A

The determinant of the matrix 1230-46005is

• b) -4

• c) 5

• d) -20

Rank of null matrix is

• 0

• b. 1

• c. ∞

• d. None

A square matrix is orthogonal if

• AAT= I

• b) AA= I

• c) AT=-A

• d) A2=A

Dimension of a vector space V = 0 is

• 0

• b) 1

• c) ∞

• d) none of them.

If 0 is the zero vector in a vector space V over F, which of the following is true?

• It is always linear independent.

• It is always linearly dependent.

• It is never linearly dependent.

• It is sometimes linear dependent.

The dimension of the vector space of all 2 X 3 matrices is

• 6

• b. 5

• c. 2

• d. 3