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IITM BS Week 4 Mathematics 2 Questions | Prasnya
Mathematics 2 > Week 4
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27Q
01
Choose all the subspaces isomorphic to
R
3
\mathbb{R}^3
R
3
from the options given below.
Multiple correct
MEDIUM
6 marks
10 May 2026
02
Choose all the subspaces isomorphic to
R
3
\mathbb{R}^3
R
3
.
Multiple correct
HARD
7 marks
10 May 2026
03
Find the rank of A.
Comprehension
EASY
4 marks
10 May 2026
04
Find the rank of B.
Comprehension
EASY
4 marks
10 May 2026
05
Let A =
[
1
2
3
3
2
1
a
a
a
2
4
k
]
\begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \\ a & a & a \\ 2 & 4 & k \end{bmatrix}
1
3
a
2
2
2
a
4
3
1
a
k
. Choose the correct option.
Single correct
MEDIUM
5 marks
21 December 2025
06
Find the dimension of the subspace W = {(x, y, z, w) in
R
4
\mathbb{R}^4
R
4
| x + y - z + w = 0, w - y - 3x = 0, and 3z/2 + w - y = 0}.
Numerical
MEDIUM
6 marks
21 December 2025
07
Let A =
[
1
−
2
3
4
v
1
v
2
]
\begin{bmatrix} 1 & -2 & 3 \\ 4 & v_1 & v_2 \end{bmatrix}
[
1
4
−
2
v
1
3
v
2
]
. Choose the correct option.
Single correct
MEDIUM
5 marks
21 December 2025
08
Which of the following options are correct?
Multiple correct
MEDIUM
3 marks
31 August 2025
09
Let
T
:
R
3
→
R
T: \mathbb{R}^3 \to \mathbb{R}
T
:
R
3
→
R
^
3
3
3
be a linear transformation such that T(1, 0, 0) =
(
2
,
−
1
,
1
)
(2, -1, 1)
(
2
,
−
1
,
1
)
and T(0, 1, 0) =
(
3
,
0
,
1
)
(3, 0, 1)
(
3
,
0
,
1
)
. Choose all suitable answers for T(0, 0, 1) such that T is invertible.
Multiple correct
MEDIUM
3 marks
31 August 2025
10
What is the maximum rank of A?
Comprehension
EASY
1 marks
13 April 2025
11
Find the dimension of W.
Comprehension
EASY
1 marks
13 April 2025
12
Let
U
=
{
(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
U = \{(x, y, z) \in \mathbb{R}^3 \mid x + y + z = 0\}
U
=
{(
x
,
y
,
z
)
∈
R
3
∣
x
+
y
+
z
=
0
}
. Which of the following sets represents
W
∩
U
W \cap U
W
∩
U
?
Comprehension
MEDIUM
1 marks
13 April 2025
13
Consider the subspace W = {(x, y, z, w) | x + y = z, z + w = y - x} of
R
4
\mathbb{R}^4
R
4
. Find the dimension of W.
Single correct
MEDIUM
2 marks
22 December 2024
14
The columns of A span
R
2
\mathbb{R}^2
R
2
for all values of k.
Comprehension
MEDIUM
1 marks
22 December 2024
15
The rank of A is 1 for some k.
Comprehension
EASY
1 marks
22 December 2024
16
Let S = {u1, u2, u3, u4, u5} be a linearly independent subset of a vector space V. Select all true statements.
Multiple correct
EASY
3 marks
01 September 2024
17
What is the rank of x * y^T?
Comprehension
EASY
1 marks
28 April 2024
18
V = {
[
x
0
y
0
0
0
0
x
+
y
0
]
\begin{bmatrix} x & 0 & y \\ 0 & 0 & 0 \\ 0 & x+y & 0 \end{bmatrix}
x
0
0
0
0
x
+
y
y
0
0
: x, y in R }, the vector space of all 3 x 3 real matrices.
Comprehension
EASY
1 marks
28 April 2024
19
W = {(x,y,z) in
R
3
\mathbb{R}^3
R
3
: x + y - 2z = 0 and 2x - y + z = 0 and x, y, z in R}, where W is a subspace of
R
3
\mathbb{R}^3
R
3
.
Comprehension
EASY
1 marks
28 April 2024
20
Let V be a vector space and v1, v2, v3 be three distinct elements in V. If every v in V can be expressed as a unique linear combination of these three vectors, which of the following statements is true? Here,
dim
(
V
)
\dim(V)
dim
(
V
)
refers to the dimension of V.
Single correct
EASY
3 marks
24 December 2023
21
Which of the following are bases for W
Comprehension
HARD
3 marks
24 December 2023
22
What is the dimension of W?
Comprehension
EASY
1 marks
24 December 2023
23
Which of the following is a basis
β
\beta
β
for W?
Comprehension
EASY
2 marks
30 April 2023
24
Find Rank(A).
Comprehension
EASY
2 marks
30 April 2023
25
Which of the following denotes the column space of A?(More than one option may be correct)
Comprehension
MEDIUM
2 marks
30 April 2023
26
Let
T
:
R
3
→
R
3
T: \mathbb{R}^3 \to \mathbb{R}^3
T
:
R
3
→
R
3
be a linear transformation whose matrix representation is
A
A
A
. Which of the following is true?
Multiple correct
MEDIUM
3 marks
11 December 2022
27
Let W be a subspace of
R
3
\mathbb{R}^3
R
3
(with inner product as the dot product) such that W = {
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
|
det
(
A
)
\text{det}(A)
det
(
A
)
= 0 }. If
β
\beta
β
is an orthonormal basis of W, then find the cardinality of the set
β
\beta
β
.
Comprehension
EASY
2 marks
07 August 2022
Showing 27 questions.
Complete question index for this section:
Question 1 (multiple):
Question 2 (multiple):
Question 3 (comprehension):
Question 4 (comprehension):
Question 5 (single):
Question 6 (integer):
Question 7 (single):
Question 8 (multiple):
Question 9 (multiple):
Question 10 (comprehension):
Question 11 (comprehension):
Question 12 (comprehension):
Question 13 (single):
Question 14 (comprehension):
Question 15 (comprehension):
Question 16 (multiple):
Question 17 (comprehension):
Question 18 (comprehension):
Question 19 (comprehension):
Question 20 (single):
Question 21 (comprehension):
Question 22 (comprehension):
Question 23 (comprehension):
Question 24 (comprehension):
Question 25 (comprehension):
Question 26 (multiple):
Question 27 (comprehension):
