Question 14 - Week 2 Practice | Prasnya
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Week 2
Question 14
00:00
Est. 2 min
Marks:
+3.00
0.00
Consider the system of linear equations
A
x
=
b
Ax=b
, where
A
∈
M
n
×
n
(
R
)
A\in M_{n\times n}(\mathbb{R})
. Which of the following conditions guarantees that the system is consistent for any
b
∈
R
n
b\in\mathbb{R}^n
? Select all true statements.
Multiple correct
Medium Difficulty
07 July 2024
A
A
A
is a diagonal matrix with non-zero diagonal entries.
B
At least one column of
A
A
is a linear combination of two other columns of
A
A
.
C
b
b
is one of the columns of
A
A
.
D
The reduced row echelon form of
A
A
has no zero rows.
E
A
A
has at least
n
−
1
n-1
linearly independent rows.
