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Question 2 - Week 2 Practice | Prasnya
Q2
00:00
15 Mar 2026
Q2.
If
A
A
A
is a
3
×
4
3\times4
3
×
4
matrix and
b
b
b
is a
3
×
1
3\times1
3
×
1
matrix, then choose the set of correct options.
A
If
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
is the augmented matrix and
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is obtained from
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
after a finite number of elementary row operations, then the systems
A
x
=
b
Ax=b
A
x
=
b
and
A
′
x
=
b
′
A'x=b'
A
′
x
=
b
′
have the same set of solutions.
B
If
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
, then the system
A
′
x
=
b
′
A'x=b'
A
′
x
=
b
′
has at least one solution.
C
If
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
, then
A
′
A'
A
′
is also in reduced row echelon form.
D
If
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
and there is no row whose only non-zero entry lies in the last column of
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
, then the system
A
x
=
b
Ax=b
A
x
=
b
has at least one solution.
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Check
Details
Q2
00:00
15 Mar 2026
Q2.
If
A
A
A
is a
3
×
4
3\times4
3
×
4
matrix and
b
b
b
is a
3
×
1
3\times1
3
×
1
matrix, then choose the set of correct options.
A
If
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
is the augmented matrix and
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is obtained from
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
after a finite number of elementary row operations, then the systems
A
x
=
b
Ax=b
A
x
=
b
and
A
′
x
=
b
′
A'x=b'
A
′
x
=
b
′
have the same set of solutions.
B
If
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
, then the system
A
′
x
=
b
′
A'x=b'
A
′
x
=
b
′
has at least one solution.
C
If
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
, then
A
′
A'
A
′
is also in reduced row echelon form.
D
If
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
is the reduced row echelon form of
(
A
∣
b
)
(A\mid b)
(
A
∣
b
)
and there is no row whose only non-zero entry lies in the last column of
(
A
′
∣
b
′
)
(A'\mid b')
(
A
′
∣
b
′
)
, then the system
A
x
=
b
Ax=b
A
x
=
b
has at least one solution.
Save
Check
Details
