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Week 1 Practice Questions | Prasnya
Q1
00:00
15 Mar 2026
Q1.
Let
A
=
[
1
a
a
2
a
3
1
b
b
2
b
3
1
c
c
2
c
3
1
d
d
2
d
3
]
A=\begin{bmatrix}1&a&a^2&a^3\\1&b&b^2&b^3\\1&c&c^2&c^3\\1&d&d^2&d^3\end{bmatrix}
A
=
1
1
1
1
a
b
c
d
a
2
b
2
c
2
d
2
a
3
b
3
c
3
d
3
where
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are distinct real numbers. Which of the following statements are correct?
A
If the sum of every row of
A
A
A
is
0
0
0
, then
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
.
B
det
(
A
)
\det(A)
det
(
A
)
changes sign if rows
2
2
2
and
4
4
4
are interchanged.
C
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
if any two of the numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are equal.
D
det
(
A
)
\det(A)
det
(
A
)
changes sign if each row is multiplied by
−
1
-1
−
1
.
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Check
Details
Q1
00:00
15 Mar 2026
Q1.
Let
A
=
[
1
a
a
2
a
3
1
b
b
2
b
3
1
c
c
2
c
3
1
d
d
2
d
3
]
A=\begin{bmatrix}1&a&a^2&a^3\\1&b&b^2&b^3\\1&c&c^2&c^3\\1&d&d^2&d^3\end{bmatrix}
A
=
1
1
1
1
a
b
c
d
a
2
b
2
c
2
d
2
a
3
b
3
c
3
d
3
where
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are distinct real numbers. Which of the following statements are correct?
A
If the sum of every row of
A
A
A
is
0
0
0
, then
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
.
B
det
(
A
)
\det(A)
det
(
A
)
changes sign if rows
2
2
2
and
4
4
4
are interchanged.
C
det
(
A
)
=
0
\det(A)=0
det
(
A
)
=
0
if any two of the numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are equal.
D
det
(
A
)
\det(A)
det
(
A
)
changes sign if each row is multiplied by
−
1
-1
−
1
.
Save
Check
Details
