Question 1 - Week 1 Practice | Prasnya
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Week 1
Question 1
00:00
Est. 3 min
Marks:
+5.00
0.00
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}
where
a
,
b
,
c
,
d
a,b,c,d
are distinct real numbers. Which of the following statements are correct?
Multiple correct
Medium Difficulty
15 March 2026
A
If the sum of every row of
A
A
is
0
0
, then
det
(
A
)
=
0
\det(A)=0
.
B
det
(
A
)
\det(A)
changes sign if rows
2
2
and
4
4
are interchanged.
C
det
(
A
)
=
0
\det(A)=0
if any two of the numbers
a
,
b
,
c
,
d
a,b,c,d
are equal.
D
det
(
A
)
\det(A)
changes sign if each row is multiplied by
−
1
-1
.
