Question 2 MCQ · 4.0 marks
Only S1 is correct.
Only S2 is correct.
Only S1 and S3 are correct.
Only S1 and S2 are correct.
S1, S2, and S3 are all correct.
A published solution is not available for this question yet.
Mathematics for Data Science II · Quiz 1 · Jan 2026
Mathematics for Data Science II · Quiz 1 · Jan 2026
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Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.
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Question 3 MCQ · 4.0 marks
Consider a subspace
of
. Which of the
following options describes a basis of
?
.
.
.
A published solution is not available for this question yet.
Question 4 MSQ · 4.0 marks
Which of the following subsets are subspaces of
under the usual addition and scalar
multiplication?
.
.
.
.
A published solution is not available for this question yet.
Question 5 MSQ · 5.0 marks
Let
where
are distinct real numbers.
Which of the following statements are **correct**?
If the sum of every row of
is
, then
is
.
changes sign if rows 2 and 4 are interchanged.
if any two of the numbers
are equal.
changes sign if each row is multiplied by
.
A published solution is not available for this question yet.
Question 6 MSQ · 5.0 marks
If
is a
matrix and
is a
matrix, then choose the set of correct options.
If
is the augmented matrix and
is the matrix obtained from
after a finite number of elementary row operations, then the system
and the
system
have the same set of solutions.
If
is the reduced row echelon form of
, then the system
has at least one solution.
If
is the reduced row echelon form of
, then
is also in reduced
row echelon form.
If
is the reduced row echelon form of
and there is no row such
that the only non zero entry lies in the last column of
, then the system
has at least
one solution.
A published solution is not available for this question yet.
Question 7 NAT · 4.0 marks
A company produces two types of gadgets, A and B.
• Each gadget A requires 2 hours of assembly and 3 hours of testing.
• Each gadget B requires 3 hours of assembly and 2 hours of testing.
The company has 8 hours of assembly and 7 hours of testing available per week. The profit from
gadget A is Rs 5, and from gadget B is Rs 4.
Determine the **total profit** if the company uses all available assembly and testing hours.
A published solution is not available for this question yet.
Question 8 NAT · 4.0 marks
Suppose
and
. Let
be a vector defined as
such
that
and
. Find the value of
.
A published solution is not available for this question yet.
Question 9 NAT · 4.0 marks
Suppose the vectors
,
and
in
are linearly dependent. Find the
value of
.
A published solution is not available for this question yet.
Question 10 NAT · 4.0 marks
Consider a shop that sells muffins, cookies, and cakes. The total sales on three consecutive days
are as follows:
• On Monday, 1 muffin, 2 cookies, and 3 cakes were sold for a total of 140.
• On Tuesday, 2 muffins, 1 cookie, and 4 cakes were sold for a total of 160.
• On Wednesday, 3 muffins, 3 cookies, and 5 cakes were sold for a total of 240.
Let
,
, and
denote the price of a muffin, a cookie, and a cake, respectively. Formulate a system
of linear equations representing the above scenario and find the value of
.
A published solution is not available for this question yet.
Question 11 NAT · 2.0 marks
Suppose the rank of the matrix
is
.
Based on the above data, answer the given subquestions.
Find
.
A published solution is not available for this question yet.
Question 12 NAT · 2.0 marks
Suppose the rank of the matrix
is
.
Based on the above data, answer the given subquestions.
Find
.
A published solution is not available for this question yet.
Question 13 MCQ · 4.0 marks
Consider a subset
of
.
Based on the above data, answer the given subquestions.
Which of the following options is correct?
A published solution is not available for this question yet.
Question 14 NAT · 4.0 marks
Consider a subset
of
.
Based on the above data, answer the given subquestions.
Consider the vector space
with the addition and scalar multiplication operations from
the correct option of the previous question. What is the dimension of the vector space?
A published solution is not available for this question yet.