Question 29 - Week 3 Practice | Prasnya
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Week 3
Question 29
00:00
Est. 3 min
Marks:
+4.00
0.00
Choose the set of correct options.
Multiple correct
Medium Difficulty
05 June 2022
A
If
v
v
and
w
w
are linearly independent, then
v
+
w
v+w
and
w
w
are also linearly independent.
B
If
A
n
=
0
A^n=0
for some
2
×
2
2\times2
matrix
A
A
and some non-zero natural number
n
n
, then
A
A
must be the zero matrix of order
2
2
.
C
If a homogeneous system of linear equations
A
x
=
0
Ax=0
has a non-zero solution, then it must have infinitely many solutions.
D
If
A
3
=
I
A^3=I
for some
n
×
n
n\times n
matrix
A
A
, then it is not necessary that
A
2
A^2
is an invertible matrix.
