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Virtual University of Pakistan For any subspace W of a vector space V, which one is not the axiom for subspace.

0 must be in W. For all u, v in W and u – v must be in W. For all u, v in W and u.v must be in W. For any scalar k and u in W then k.u in W.

Which one is not the axiom for vector space?

0 + u = u

0.u = u

1. u = u

u + v = v + u

TRUE

FALSE

At what condition det(AB)=(detA)(detB) is possible?

When A and B are n x n matrices

When A is a row matrix When A and B are m x n matrices When B is a column matrix

which of the following condition is true?

detB = detA

detA detB = 0

TRUE

FALSE While using the Cramer’s rule, if determinant D = 0, and other determinant is not zero then how many solutions are there? Many solutions

No solution

Two solutions One solution

Which of the following is all permutations of {1,2}?

(1,2,2,1)

Q1. of 10 ( Start time: 09:52:17 PM ) Total Marks: 1

FALSE

TRUE

Q2. of 10 ( Start time: 09:53:11 PM ) Total Marks: 1

which of the following condition is true?

detB = detA detA detB = 0

Q3. of 10 ( Start time: 09:54:09 PM ) Total Marks: 1

At what condition the Cramer’s formula is valid for linear systems?

When matrix is n x n

When det(A) is equal to zero When matrix is m x n When det(A) in not equal to zero

Q4. of 10 ( Start time: 09:54:44 PM ) Total Marks: 1

A matrix has not the same determinant if we add a multiple of a column to another column.