A quiz from Lecture 07-08 will be started on May 03,2014 at 12:01AM, its due date is May 09, 2014 (11:59PM). So to avoid any inconvenience in VULMS, you are advised to attempt the quiz before 2 days of Deadline, after 7^{th} of May 2014 no complain will be entertained.
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MIDTERM EXAMINATION
MTH501- Linear Algebra (MCQ’s File)
Question No: 1
If for a linear transformation the equation T(x )= 0 has only the trivial solution then T is
► one-to-one
► onto
Question No: 2
Which one of the following is an matrix?
►
►
►
►
Question No: 3
Let and let k be a scalar .A formula that relates det kA to k and det A is
► det kA= k det A
► det kA = det (k+A)
► det k A = k^{2} det A
► det kA = det A
Question No:
The equation x = p + t v describes a line
► through v parallel to p
► through p parallel to v
► through origin parallel to p
Question No: 5
Determine which of the following sets of vectors are linearly dependent.
►
►
►
Question No: 6
Every linear transformation is a matrix transformation
► True
► False
Question No: 7
A null space is a vector space.
► True
► False
Question No: 8
If two row interchanges are made in succession, then the new determinant
► equals to the old determinant
► equals to -1 times the old determinant
Question No: 9
The determinant of A is the product of the pivots in any echelon form U of A , multiplied by (-1)^{r} , Where r is
► the number of rows of A
► the number of row interchanges made during row reduction from A to U
► the number of rows of U
► the number of row interchanges made during row reduction U to A
Question No: 10
If A is invertible, then det(A)det(A^{-1})=1.
► True
► False
Question No: 11
A square matrix is lower triangular if and only if for
►
►
►
►
Question No: 12
The product of upper triangular matrices is
► lower triangular matrix
► upper triangular matrix
► diagonal matrix
Question No: 13
The matrix multiplication is associative
► True
► False
Question No: 14
We can add the matrices of ______________.
► same order
► same number of columns.
► same number of rows
► different order
Question No: 15
By solving system of equations with iterative method, we stop the process when the entries in two successive iterations are ________.
► repeat
► large difference
► different
► Same
Question No: 16
Jacobi’s Method is ____________ converges to solution than Gauss Siedal Method.
► slow
► fast
► better
Question No: 17
A system of linear equations is said to be homogeneous if it can be written in the form ______________.
► AX = B
► AX = 0
► AB = X
► X = A^{-1}
Question No: 18
The row reduction algorithm applies only to augmented matrices for a linear system.
► True
► False
Question No: 19
Whenever a system has no free variable, the solution set contains many solutions.
► True
► False
Question No: 20
Which of the following is not a linear equation?
►
►
►
►
Question No: 21
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 No: 22
The determinant of a diagonal matrix is the product of the diagonal elements.
Select correct option:
Question No: 23
By using determinants, we can easily check that the solution of the given system of linear equation exits and it is unique.
Question No: 24
A matrix A and its transpose have the same determinant.
Question No: 25
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?
Question No: 26
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.
Question No: 27
How many different permutations are there in the set of integers {1,2,3}?
Question No: 28
If A is n x n matrix and det (A) = 2 then det (5A) = ________.
Question No: 29
Every vector space has at least two subspaces; one is itself and the second is:
Question No: 30
If one row of A is multiplied by k to produce B, then which of the following condition is true?
Select correct option:
SOLVED MTH 501 CURRENT QUIzz
Question # 1 of 10 ( Start time: 08:24:19 PM ) Total Marks: 1
Two vectors u and v are orthogonal to each other if ___________.
Select correct option:
u . v = 0
u . v = 1
u + v = 0
u - v = 0
Question # 2 of 10 ( Start time: 08:25:33 PM ) Total Marks: 1
If the columns of a matrix are linearly independent then the matrix is ________.
Select correct option:
invertible (A) is invertible if A has linearly independent columns in Matrics.
symmetric
antisymmetric
singular
Question # 3 of 10 ( Start time: 08:27:06 PM ) Total Marks: 1
If the columns of a matrix are ______ then the matrix is invertible.
Select correct option:
linearly independent (A) is invertible if A has linearly independent columns in
Matrics.
linearly dependent
Question # 4 of 10 ( Start time: 08:28:38 PM ) Total Marks: 1
An n x n matrix A is _______ if and only if A has n linearly independent vectors.
Select correct option:
diagonalizable
singular not sure
symmetric
scalar
Question # 7 of 10 ( Start time: 08:31:46 PM ) Total Marks: 1
Two vectors are _______if at least one of the vector is a multiple of the other
Select correct option:
linearly independent Page no 89
linearly dependent
Question # 8 of 10 ( Start time: 08:32:49 PM ) Total Marks: 1
An n x n matrix with n distinct eigen values is diagonalizable.
Select correct option:
TRUE Page no 402
FALSE
Question # 9 of 10 ( Start time: 08:33:50 PM ) Total Marks: 1
2x – 3y = –2 4x + y = 24 The above system has a ______ solution.
Select correct option:
inconsistant
many
unique
trivial
Question # 10 of 10 ( Start time: 08:35:02 PM ) Total Marks: 1
An n x n matrix A is ___ if and only if 0 is not an eigen value of A.
Select correct option:
invertible In invertible Matrix Theorem.. The n × n matrix A is invertible if and
only if 0 is not an eigenvalue of A
singular
symmetric
scalar
some more solved Quizz..
Mth501_Linear Algebra
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 Gauss-Seidel 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 Gauss-Seidel 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
Malika Eman gud keep it up & thanks for sharing
This subject hv very limited MCQs...
so, i'm giving u some very imp links to having Linear Algebra Solved Quizz.u can prepare it for also Exams preparation.
for the Quizz
http://www.math.jhu.edu/mathcourses/201/Quizzes/
http://www.maths.usyd.edu.au/u/UG/JM/MATH1002/Quizzes/
https://www2.bc.edu/~yucei/Spring11/MT2100102/mt210test.html
http://www.math.toronto.edu/burbulla/quizz188.pdf
Gud Luck!
thanks malika
Please all students related this subject Share your online Quizzes here to help each other.thanks
Please share the question and their answers of this quiz if anyone has done.
Thanks.
MTH501_Online_Quiz_02
See the attached file please
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