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IITM BS Week 3 Mathematics 2 Questions | Prasnya
Mathematics 2 > Week 3
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11Q
01
Let Ax = b represent a system of m linear equations in n variables. Choose the correct options.
Multiple correct
MEDIUM
8 marks
21 December 2025
02
Find the set of all real values of
α
\alpha
α
for which the columns of the matrix
M
=
[
1
0
3
α
2
α
2
0
−
α
α
]
M = \begin{bmatrix} 1 & 0 & 3 \\ \alpha & 2 & \alpha^2 \\ 0 & -\alpha & \alpha \end{bmatrix}
M
=
1
α
0
0
2
−
α
3
α
2
α
are linearly dependent.
Single correct
MEDIUM
1 marks
13 April 2025
03
Find the value of
t
∈
R
t \in \mathbb{R}
t
∈
R
such that
v
3
∈
span
{
v
1
,
v
2
}
v_3 \in \text{span}\{v_1, v_2\}
v
3
∈
span
{
v
1
,
v
2
}
.
Comprehension
EASY
1 marks
13 April 2025
04
Let
v
1
,
v
2
,
v
3
v_1, v_2, v_3
v
1
,
v
2
,
v
3
be as in the main question with the value of
t
t
t
obtained. If
v
3
=
α
v
1
+
β
v
2
v_3 = \alpha v_1 + \beta v_2
v
3
=
α
v
1
+
β
v
2
, find
α
−
β
\alpha - \beta
α
−
β
.
Comprehension
EASY
1 marks
13 April 2025
05
Let
A
A
A
be a
3
×
3
3 \times 3
3
×
3
matrix such that
v
1
v_1
v
1
and
v
2
v_2
v
2
are the first 2 columns of
A
A
A
. Choose the correct option from the following.
Comprehension
MEDIUM
1 marks
13 April 2025
06
Assume the usual vector addition and scalar multiplication for all the options below. Choose the correct option(s) from the following statements.
Multiple correct
MEDIUM
3 marks
22 December 2024
07
When k = 1/3, the row vectors span the plane in
R
3
\mathbb{R}^3
R
3
given by the equation x - 3y = 0.
Comprehension
MEDIUM
1 marks
22 December 2024
08
Let S = {v1, v2, v3, v4} be a subset of
R
3
\mathbb{R}^3
R
3
. Select all true statements.
Single correct
EASY
2 marks
28 April 2024
09
Let V be the vector space of all n x n matrices with usual addition and scalar multiplication. Which of the following subset(s) form a subspace of V?
Multiple correct
EASY
2 marks
03 September 2023
10
Let
W
=
span
{
(
1
,
1
,
1
)
,
(
1
,
−
1
,
0
)
}
W = \text{span}\{(1, 1, 1), (1, -1, 0)\}
W
=
span
{(
1
,
1
,
1
)
,
(
1
,
−
1
,
0
)}
in
R
3
\mathbb{R}^3
R
3
. Find the projection of
v
=
(
1
,
2
,
3
)
v = (1, 2, 3)
v
=
(
1
,
2
,
3
)
onto
W
W
W
.
Multiple correct
MEDIUM
3 marks
03 September 2023
11
Some of the conditions that need to be checked to identify a vector space V are: . (Enter 5 best possible options. Enter only the serial numbers of those options in increasing order without adding any comma or space in between them.)
Comprehension
MEDIUM
2 marks
30 April 2023
Showing 11 questions.
Complete question index for this section:
Question 1 (multiple):
Question 2 (single):
Question 3 (comprehension):
Question 4 (comprehension):
Question 5 (comprehension):
Question 6 (multiple):
Question 7 (comprehension):
Question 8 (single):
Question 9 (multiple):
Question 10 (multiple):
Question 11 (comprehension):
