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IITM BS Week 5 Mathematics 2 Questions | Prasnya
Mathematics 2 > Week 5
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10Q
01
If A is an orthogonal matrix of order 5, then find the nullity of the matrix A.
Numerical
EASY
5 marks
10 May 2026
02
Let
T
:
R
3
→
R
2
T: \mathbb{R}^3 \to \mathbb{R}^2
T
:
R
3
→
R
2
be a linear transformation given by
T
(
1
,
0
,
1
)
=
(
1
,
0
)
T(1,0,1) = (1,0)
T
(
1
,
0
,
1
)
=
(
1
,
0
)
,
T
(
1
,
1
,
0
)
=
(
0
,
1
)
T(1,1,0) = (0,1)
T
(
1
,
1
,
0
)
=
(
0
,
1
)
and
T
(
0
,
1
,
1
)
=
(
a
,
b
)
T(0,1,1) = (a, b)
T
(
0
,
1
,
1
)
=
(
a
,
b
)
. If
T
(
1
,
2
,
−
3
)
=
(
a
,
b
)
T(1,2,-3) = (a, b)
T
(
1
,
2
,
−
3
)
=
(
a
,
b
)
, find
a
−
b
a - b
a
−
b
.
Numerical
HARD
6 marks
10 May 2026
03
Let
T
:
R
3
→
R
3
T: \mathbb{R}^3 \to \mathbb{R}^3
T
:
R
3
→
R
3
be a linear transformation given by
T
(
1
,
0
,
0
)
=
(
1
,
0
,
0
)
T(1,0,0) = (1,0,0)
T
(
1
,
0
,
0
)
=
(
1
,
0
,
0
)
,
T
(
1
,
1
,
0
)
=
(
0
,
1
,
0
)
T(1,1,0) = (0,1,0)
T
(
1
,
1
,
0
)
=
(
0
,
1
,
0
)
, and
T
(
0
,
1
,
1
)
=
(
0
,
0
,
1
)
T(0,1,1) = (0,0,1)
T
(
0
,
1
,
1
)
=
(
0
,
0
,
1
)
. Choose the correct option from the following.
Single correct
MEDIUM
5 marks
10 May 2026
04
Let A be a nonzero 5 x 5 matrix such that A^2 = 0. Find the maximum possible rank of A.
Numerical
MEDIUM
2 marks
31 August 2025
05
Find the expression for T(x,y).
Comprehension
MEDIUM
1 marks
13 April 2025
06
What is the minimum value for nullity of A?
Comprehension
EASY
1 marks
13 April 2025
07
How many solutions does Ax = 0 have?
Comprehension
EASY
1 marks
28 April 2024
08
How many solutions does A^T * x = 0 have?
Comprehension
MEDIUM
1 marks
28 April 2024
09
Find the dimension of the solution space of the homogeneous equation
B
x
=
0
Bx = 0
B
x
=
0
.
Comprehension
EASY
1 marks
24 December 2023
10
Which of the following sets denotes nullspace(A)?
Comprehension
EASY
2 marks
30 April 2023
Showing 10 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (integer):
Question 3 (single):
Question 4 (integer):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (comprehension):
Question 9 (comprehension):
Question 10 (comprehension):
