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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
The GaussSeidel method is applicable to strictly diagonally dominant matrix.
TRUE
FALSE
By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.
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
For any 3x3 matrix A where det (A) = 3, then det (2A) = ________.
24
20
15
6
If a multiple of one row of a square matrix A is added to another row to produce a matrix B, then which of the following condition is true?
detB = detA
detB = k detA
detA detB = 0
detA detB = detA
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
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)
Question # 1 of 10 ( Start time: 09:52:17 PM ) 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 # 2 of 10 ( Start time: 09:53:11 PM ) Total Marks: 1
If a multiple of one row of a square matrix A is added to another row to produce a matrix B, then which of the following condition is true?
Select correct option:
detB = k detA
detB = detA
detA detB = 0
detA detB = detA
Question # 3 of 10 ( Start time: 09:54:09 PM ) Total Marks: 1
At what condition the Cramer’s formula is valid for linear systems?
Select correct option:
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
Question # 4 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.
Select correct option:
TRUE
FALSE
Question # 5 of 10 ( Start time: 09:55:30 PM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
Select correct option:
TRUE
FALSE
Question # 6 of 10 ( Start time: 09:56:10 PM ) Total Marks: 1
Which of the following is the volume of the parallelepiped determined by the columns of A where A is a 3 x 3 matrix?
Select correct option:
det A
[A]
det A
A^(1) ,that is inverse of A
Question # 7 of 10 ( Start time: 09:57:25 PM ) Total Marks: 1
For any 3x3 matrix A where det (A) = 3, then det (2A) = ________.
Select correct option:
24
20
15
6
Question # 8 of 10 ( Start time: 09:58:24 PM ) Total Marks: 1
Which one is not the axiom for vector space?
Select correct option:
0 + u = u
0.u = u
1.u = u
u + v = v + u
2
Question # 9 of 10 ( Start time: 09:58:58 PM ) Total Marks: 1
Which of the following is NOT the axiom for vector space where u, v, w in V are set of vectors and l, m, n are scalars?
Select correct option:
u + (v + w) = (u + v) + w
u.v =v.u
l (u + v)= l u + l v
(l +m) u= I u+ m u
Question # 10 of 10 ( Start time: 09:59:48 PM ) Total Marks: 1
If two rows or columns of a square matrix are identical, then det (A)wil be _______.
Select correct option:
zero
non zero
one
positive
Question # 1 of 10 ( Start time: 10:30:38 PM ) Total Marks: 1
If A is strictly diagonally dominant, then A is _________.
Select correct option:
invertible
singular
symmetric
scalar
Question # 2 of 10 ( Start time: 10:31:17 PM ) Total Marks: 1
The GaussSeidel method is applicable to strictly diagonally dominant matrix.
Select correct option:
TRUE
FALSE
Question # 3 of 10 ( Start time: 10:32:00 PM ) Total Marks: 1
If the absolute value of each diagonal entry exceeds the sum of the absolute values of the other entries in the same row then a matrix A is called:
Select correct option:
invertible
strictly diagonally dominant
diagonally
scalar
Question # 4 of 10 ( Start time: 10:33:26 PM ) Total Marks: 1
The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal.
Select correct option:
TRUE
FALSE
Question # 5 of 10 ( Start time: 10:33:52 PM ) Total Marks: 1
Which one is not the axiom for vector space?
Select correct option:
0 + u = u
0.u = u
1.u = u
u + v = v + u
Question # 6 of 10 ( Start time: 10:34:16 PM ) Total Marks: 1
Let W = {(x, y) such that x, y in R and x = y}. Is W a vector subspace of plane.
Select correct option:
YES
NO
Question # 7 of 10 ( Start time: 10:34:58 PM ) Total Marks: 1
If A is a triangular matrix, then det(A) is the product of the entries on the ________.
Select correct option:
main diagonal of A
first two rows of A
diagonal of A
first two columns of A
Question # 8 of 10 ( Start time: 10:35:59 PM ) 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 # 9 of 10 ( Start time: 10:36:55 PM ) Total Marks: 1
If a matrix A is invertible than adj(A) is also invertible.
Select correct option:
TRUE
FALSE
Question # 10 of 10 ( Start time: 10:37:57 PM ) Total Marks: 1
If all the entries of a row or a column of a square matrix are zero, then det (A) will be _____________.
Select correct option:
zero
infinity
one
non zero

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For which of the matrix, the GaussSeidel method is applicable
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Consider a system of linear equations A x =b where A is a3 ×3 matrix having 3 pivot positions, then which
statement is false about the system Ax =b
(a) System has unique solution.
(b) Rank of the matrix is 3.
(c) There is only one free variable in solution of that system.
(d) The associated homogeneous system Ax =0 has only trivial system.
If a finite set S of non zero vectors span a vector space V, then some subset of S is a basis for V.
1. True
2. false
D
If rank of a3 x 5 matrix is 3 then dimension of its Null space is
(a) 0
(b) 3
(c) 2
(d) We can’t say anything
1
If matrix A has zero as an eigenvalue then which statement(s) about A must be true.
I. Matrix A is not invertible.
II. Matrix A will also have an eigenvalue 2.
III. Matrix is diagonalizable.
1 II and III only.
2 I only. (true)
3 II and III only.
4 All three.
1 x 3
3 x 1
3 x 3
4 x 1
Determinant of a noninvertible(singular) matrix always
► vanish
► unity
► non zero negative
► non zero positive
Rank of a zero matrix of any order is
► zero
► three
► four
► nine
► Zero
► One
► Two
► Three
► Are orthogonal
►Having their inner product zero
► Can span a subspace while both passing through the origin
► All above statements are equivalent
thanks
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