Question 2 - Week 2 Practice | Prasnya
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Week 2
Question 2
00:00
Est. 3 min
Marks:
+5.00
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If
A
A
is a
3
×
4
3\times4
matrix and
b
b
is a
3
×
1
3\times1
matrix, then choose the set of correct options.
Multiple correct
Medium Difficulty
15 March 2026
A
If
(
A
∣
b
)
(A\mid b)
is the augmented matrix and
(
A
′
∣
b
′
)
(A'\mid b')
is obtained from
(
A
∣
b
)
(A\mid b)
after a finite number of elementary row operations, then the systems
A
x
=
b
Ax=b
and
A
′
x
=
b
′
A'x=b'
have the same set of solutions.
B
If
(
A
′
∣
b
′
)
(A'\mid b')
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
, then the system
A
′
x
=
b
′
A'x=b'
has at least one solution.
C
If
(
A
′
∣
b
′
)
(A'\mid b')
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
, then
A
′
A'
is also in reduced row echelon form.
D
If
(
A
′
∣
b
′
)
(A'\mid b')
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
and there is no row whose only non-zero entry lies in the last column of
(
A
′
∣
b
′
)
(A'\mid b')
, then the system
A
x
=
b
Ax=b
has at least one solution.
