# 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 ……….
0
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
0

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 ……….
0
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$\begin{bmatrix}1&4\\2&5\\3&6\end{bmatrix}?$
0
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
0

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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