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Question 29 - Week 3 Practice | Prasnya
Q29
00:00
5 Jun 2022
Q29.
Choose the set of correct options.
A
If
v
v
v
and
w
w
w
are linearly independent, then
v
+
w
v+w
v
+
w
and
w
w
w
are also linearly independent.
B
If
A
n
=
0
A^n=0
A
n
=
0
for some
2
×
2
2\times2
2
×
2
matrix
A
A
A
and some non-zero natural number
n
n
n
, then
A
A
A
must be the zero matrix of order
2
2
2
.
C
If a homogeneous system of linear equations
A
x
=
0
Ax=0
A
x
=
0
has a non-zero solution, then it must have infinitely many solutions.
D
If
A
3
=
I
A^3=I
A
3
=
I
for some
n
×
n
n\times n
n
×
n
matrix
A
A
A
, then it is not necessary that
A
2
A^2
A
2
is an invertible matrix.
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Check
Details
Q29
00:00
5 Jun 2022
Q29.
Choose the set of correct options.
A
If
v
v
v
and
w
w
w
are linearly independent, then
v
+
w
v+w
v
+
w
and
w
w
w
are also linearly independent.
B
If
A
n
=
0
A^n=0
A
n
=
0
for some
2
×
2
2\times2
2
×
2
matrix
A
A
A
and some non-zero natural number
n
n
n
, then
A
A
A
must be the zero matrix of order
2
2
2
.
C
If a homogeneous system of linear equations
A
x
=
0
Ax=0
A
x
=
0
has a non-zero solution, then it must have infinitely many solutions.
D
If
A
3
=
I
A^3=I
A
3
=
I
for some
n
×
n
n\times n
n
×
n
matrix
A
A
A
, then it is not necessary that
A
2
A^2
A
2
is an invertible matrix.
Save
Check
Details
