MTH501 Quiz No.1 Shared by BC100400183 : Manza Ali

Question # 1 of 10 ( Start time: 10:51:24 AM )  Total Marks:  1 

If a system of equations is solved using the Gauss-Seidel method, then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix ?

Select correct option: 

 All of its entries on the diagonal must be zero.

 All of its entries below the diagonal must be zero.

 All of its entries above the diagonal must be zero.

 All of its entries below and above the diagonal must be zero.

Question # 2 of 10 ( Start time: 10:52:56 AM )  Total Marks:  1 

The determinant of a diagonal matrix is the product of the diagonal elements.

Select correct option: 

 TRUE

 FALSE

Question # 3 of 10 ( Start time: 10:54:19 AM )  Total Marks:  1 

By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique. 

Select correct option: 

 FALSE

 TRUE

Question # 4 of 10 ( Start time: 10:55:34 AM )  Total Marks:  1 

A matrix A and its transpose have the same determinant. 

Select correct option: 

 TRUE

 FALSE

Question # 5 of 10 ( Start time: 10:56:43 AM )  Total Marks:  1 

If both the Jacobi and Gauss-Seidel sequences converge for the solution of Ax=b, for any initial x(0), then which of the following is true about both the solutions?

Select correct option: 

 No solution

 Unique solution

 Different solutions

 Infinitely many solutions

Question # 6 of 10 ( Start time: 11:00:09 AM )  Total Marks:  1 

The value of the determinant of a square matrix remains unchanged if we multiply each element of a row or a column by some scalar.

Select correct option: 

 TRUE

 FALSE

Question # 7 of 10 ( Start time: 11:01:33 AM )  Total Marks:  1 

How many different permutations are there in the set of integers {1,2,3}?

Select correct option: 

 2

 4

 6

 8

 Question # 8 of 10 ( Start time: 11:02:22 AM )  Total Marks:  1 

If A is n x n matrix and det (A) = 2 then det (5A) = ________.

Select correct option: 

 10

 32

 5

 8

Question # 9 of 10 ( Start time: 11:05:30 AM )  Total Marks:  1 

Every vector space has at least two subspaces; one is itself and the second is:

Select correct option: 

 multiplication of vectors

 addition of vectors

 subspace {0}

 scalar multiplication of vectors

Question # 10 of 10 ( Start time: 11:06:56 AM )  Total Marks:  1 

If one row of A is multiplied by k to produce B, then which of the following condition is true?

 Select correct option: 

 det(AB) = (detA)(detB)

 detB = k detA

 detB = – detA

 detB = detA