# MTH212 TMA

Q1 The dimesion of the range of T is the same as the ……… of T

rank

kernel

nullity

element

Q2 The determinant of \[\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}\] is ……….

1

2

10

Q3 A square matrix the same as its tranpose is ………..

transpose

square

symmetric

asymmetric

Q4 The transpose of \[\begin{bmatrix}1&2&4\\3&2&8\\-3&6&7\\1&-1&-2\end{bmatrix}\] is

\[\begin{bmatrix}1&3&-3&-1\\2&-2&6&-1\\4&8&7&-2\end{bmatrix}\]

\[\begin{bmatrix}1&3&-3&1\\2&2&6&-1\end{bmatrix}\]

\[\begin{bmatrix}1&2&4\\3&2&8\\-3&6&7\end{bmatrix}\]

\begin{bmatrix}1&3&-3&1\\2&2&6&-1\\4&8&7&-2\end{bmatrix}

Q5 When the number of rows of a matrix is equal to the number of its columns,the…… matrix is obtained.

transpose

square

symmetric

asymmetric

Q6 The ……. of a matrix is determined by the number of its rows and columns

dimension

size

order

All of the Options

Q7 Let U and V be vector spaces over a field F and $$T : U\rightarrow V$$ be a linear transformation, then Range of T is a subspace of

T

U

V

F

Q8 The dimension of the matrix \[\begin{bmatrix}1&2&5&7\\3&2&8&-3\end{bmatrix}\] is

4 by 3

2 by 3

2by 4

3 by 2

Q9 When the rows of a matrix is interchanged by its columns, the ……. of the matrix is obtained

transpose

square

symmetric

asymmetric

Q10 Let U be a vector space over a field F,a function T(u) = u for all $$u\in U$$is called………

reflective transformation

Identity transformation

linear transformation

non linear transformation

Q1 The determinant of \[\begin{bmatrix}x&2&1\\x&5&2x\\3&x&4\end{bmatrix}\] is ………….

\[-2x^3 + x^2 + 24x+15\]

\[x^2-4x+5\]

\[x-2x\]

15

Q2 A matrix is a ……………

square array of numbers arranged in rows and columns.

circular array of numbers arranged in rows and columns.

triangular array of numbers arranged in rows and columns.

rectangular array of numbers arranged in rows and columns.

Q3 A square matrix whose tranpose is equal to the negative of the matrix itself is known as

skew-symmetric

asymmetric

symmetric

negative square

Q4 The dimension of the matrix \[\begin{bmatrix}1&2&5\\3&2&8\\1&0&-5\\-2&1&0\end{bmatrix}\] is

4 by 3

3 by 4

3 by 3

12

Q5 \[\begin{bmatrix}0&-1&3\\-1&2&5\\3&5&-4\end{bmatrix}\] is a ……….. matrix

skew-symmetric

asymmetric

symmetric

square

Q6 Given that U and V are vector spaces over a field F. Let$$T : U\rightarrow V$$ be a linear transformation, then the set $$[x\in U]T(x) = 0$$ is called the

transformation

space

kernel of T

range of T

Q7 For any linear transformation $$T : U\rightarrow V$$ , let the dimension of U be finite ,then Ker T has a …………… dimension

finite

infinite

linear

non linear

Q8 The determinant of \[\begin{bmatrix}1&2&3\\0&0&0\\7&8&9\end{bmatrix}\] is……….

12

3

1

Q9 The dimesion of the kernel of T is the same as the ……….. of T

range

rank

nullity

space

Q10 A matrix whose determinant is zero is called ……………. .

symmetric

non-symmetric

singular

non singular

Q11 The dimesion of the range of T is the same as the ……… of T

rank

kernel

nullity

element

Q12 The determinant of \[\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}\] is ……….

1

2

10

Q13 A square matrix the same as its tranpose is ………..

transpose

square

symmetric

asymmetric

Q14 The transpose of \[\begin{bmatrix}1&2&4\\3&2&8\\-3&6&7\\1&-1&-2\end{bmatrix}\] is

\[\begin{bmatrix}1&3&-3&-1\\2&-2&6&-1\\4&8&7&-2\end{bmatrix}\]

\[\begin{bmatrix}1&3&-3&1\\2&2&6&-1\end{bmatrix}\]

\[\begin{bmatrix}1&2&4\\3&2&8\\-3&6&7\end{bmatrix}\]

\begin{bmatrix}1&3&-3&1\\2&2&6&-1\\4&8&7&-2\end{bmatrix}

Q15 When the number of rows of a matrix is equal to the number of its columns,the…… matrix is obtained.

transpose

square

symmetric

asymmetric

Q16 The ……. of a matrix is determined by the number of its rows and columns

dimension

size

order

All of the Options

Q17 Let U and V be vector spaces over a field F and $$T : U\rightarrow V$$ be a linear transformation, then Range of T is a subspace of

T

U

V

F

Q18 The dimension of the matrix \[\begin{bmatrix}1&2&5&7\\3&2&8&-3\end{bmatrix}\] is

4 by 3

2 by 3

2by 4

3 by 2

Q19 When the rows of a matrix is interchanged by its columns, the ……. of the matrix is obtained

transpose

square

symmetric

asymmetric

Q20 Let U be a vector space over a field F,a function T(u) = u for all $$u\in U$$is called………

reflective transformation

Identity transformation

linear transformation

non linear transformation

Q1 The determinant of \[\begin{bmatrix}1&-2&1\\x&5&2x\\3&-x&4\end{bmatrix}\] is ………….

\[x^2\]

\[x^2-4x+5\]

\[x-2x\]

\[15\]

Q2 One of the following is not a property of determinants

Non-square matrices have no determinants

If two rows or columns are interchanged, the determinant is zero

If a row or column of a matrix is multiplied by any constant, the result is the product of the determinant and the constant

If two rows or columns are the same, the determinant is zero

Q3 What is the determinant rank of the determinant of\[\begin{bmatrix}1&4\\2&5\\3&6\end{bmatrix}?\]

1

2

3

Q4 The determinant rank of an m x n matrix A is equal to the of A.

row

rank

column

kernel

Q5 Every matrix can be reduced to a row-reduced echelon matrix by a ……………… of elementary row operations.

finite sequence

infinite sequence

sequence

series

Q6 The ………… of a row-reduced echelon matrix is equal to the number of its non-zero rows

row

rank

column

kernel

Q7 A square matrix A such that \[a_{ij}= 0 \forall i > j \] is called ………..

lower traingular

upper traingular

strictly lower traingular

strictly upper traingular

Q8 An m x n matrix A is called a row reduced echelon matrix if

the non-zero rows come before the rows

In each non-zero row, the first non-zero entry is one

the first non-zero entry in every non-zero row (after the first row ) is to the right of the first non-zero entry in the preceding row

all of the options

Q9 Let \[T \in A(V)\], then T is invertible if and only if the constant term in the minimal polynomial of T is …………..

not zero

zero

not one

one

Q10 Every vector space is isomorphic to its ……..dual.

first

second

third

fourth

Q11 The determinant of \[\begin{bmatrix}x&2&1\\x&5&2x\\3&x&4\end{bmatrix}\] is ………….

\[-2x^3 + x^2 + 24x+15\]

\[x^2-4x+5\]

\[x-2x\]

15

Q12 A matrix is a ……………

square array of numbers arranged in rows and columns.

circular array of numbers arranged in rows and columns.

triangular array of numbers arranged in rows and columns.

rectangular array of numbers arranged in rows and columns.

Q13 A square matrix whose tranpose is equal to the negative of the matrix itself is known as

skew-symmetric

asymmetric

symmetric

negative square

Q14 The dimension of the matrix \[\begin{bmatrix}1&2&5\\3&2&8\\1&0&-5\\-2&1&0\end{bmatrix}\] is

4 by 3

3 by 4

3 by 3

12

Q15 \[\begin{bmatrix}0&-1&3\\-1&2&5\\3&5&-4\end{bmatrix}\] is a ……….. matrix

skew-symmetric

asymmetric

symmetric

square

Q16 Given that U and V are vector spaces over a field F. Let$$T : U\rightarrow V$$ be a linear transformation, then the set $$[x\in U]T(x) = 0$$ is called the

transformation

space

kernel of T

range of T

Q17 For any linear transformation $$T : U\rightarrow V$$ , let the dimension of U be finite ,then Ker T has a …………… dimension

finite

infinite

linear

non linear

Q18 The determinant of \[\begin{bmatrix}1&2&3\\0&0&0\\7&8&9\end{bmatrix}\] is……….

12

3

1

Q19 The dimesion of the kernel of T is the same as the ……….. of T

range

rank

nullity

space

Q20 A matrix whose determinant is zero is called ……………. .

symmetric

non-symmetric

singular

non singular

Q1 Let U and V be finite- dimensional vector spaces over F and \[T : U\rightarrow V\] be a linear transformation , then rank(T) + nullity(T) = …….

dim(U)

ker(U)

Field(U)

zero

Q2 A linear transformation T on a finite-dimensional vector space V is …………. if and only if there exists a basis of V consisting of eigenvector of T.

finite-dimensional

linear transformation

diagonalizable

transformative

Q3 ……… theorem states that ”Every square matrix satisfies its characteristics polynomial”.

Polynomial

Isomorphic

Dual

Cayley-Hamilton

Q4 Let U and V be vector spaces over a field F. A linear transformation \[T : U\rightarrow V\] that is one – to-one is called …………..

surjective

injective

subjective

objective

Q5 Let U and V be vector spaces over a field F and dim U = n. Let \[T : U\rightarrow V\] be a linear operator, then rank (T) + nullity (T) = ………..

n

U

V

nU

Q6 Let U, V be vector spaces over a field F of dimensions m and n respectively, then L (U, V) is a vector space of dimension ……………

mn

m+n

m

n

Q7 Let U and V be vector spaces over a field F. Let \[T : U\rightarrow V\] be a one-one and onto linear transformation, then T is called ……… between U and V

monomorphism

isomorphism

dual

kernel

Q8 If \[T (\alpha _1 u_1 + \alpha _2 u_2) =\alpha _1 T (u_1) + \alpha _2 T(u_2)\], for \[\alpha _1, \alpha _2 \in F\] and \[u_1 ,u_2 \in U\] then the linear tansformation \[T : U\rightarrow F\] is known as ………..

finite-dimensional

isomorphic

linear transformation

linear functional

Q9 The space L (U,F) is the ……. of U given that U is a vector space over F

dual

isomorphic

linear functional

kernel

Q10 A linear tansformation is invertible if it is ………….

into

one-one

one-one and onto

onto

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