Question 14 - Week 4 Practice | Prasnya
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Week 4
Question 14
00:00
Est. 3 min
Marks:
+6.00
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Let
v
1
,
v
2
,
v
3
v_1,v_2,v_3
be linearly independent vectors in
R
3
\mathbb{R}^3
. Let
A
∈
M
3
×
3
(
R
)
A\in M_{3\times3}(\mathbb{R})
be a matrix such that
v
1
−
v
2
v_1-v_2
,
v
2
−
v
3
v_2-v_3
,
v
1
+
v
2
v_1+v_2
are the columns of
A
A
. Let
B
∈
M
3
×
3
(
R
)
B\in M_{3\times3}(\mathbb{R})
be a matrix such that
v
1
+
v
2
+
v
3
v_1+v_2+v_3
,
2
v
1
+
3
v
2
2v_1+3v_2
,
2
v
3
−
v
2
2v_3-v_2
are the columns of
B
B
. Which of the following options is correct?
Single correct
Medium Difficulty
23 February 2025
A
rank
(
A
)
\operatorname{rank}(A)
is
2
2
.
B
A
A
is an invertible matrix.
C
rank
(
A
)
=
rank
(
B
)
\operatorname{rank}(A)=\operatorname{rank}(B)
.
D
The system of linear equations
B
x
=
0
Bx=0
has a unique solution.
