Question 15 - Week 2 Practice | Prasnya
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Week 2
Question 15
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Est. 3 min
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Let
A
x
=
b
Ax=b
be a system of linear equations, where
A
=
[
1
0
0
−
1
0
0
1
5
0
0
0
1
]
A=\begin{bmatrix}1&0&0&-1\\0&0&1&5\\0&0&0&1\end{bmatrix}
,
x
=
[
x
1
x
2
x
3
x
4
]
T
x=\begin{bmatrix}x_1&x_2&x_3&x_4\end{bmatrix}^T
, and
b
∈
R
3
b\in\mathbb{R}^3
. Which of the following statements are true?
Multiple correct
Medium Difficulty
07 July 2024
A
A
A
is in row echelon form.
B
x
2
x_2
is an independent variable.
C
After reducing the system to reduced row echelon form, the value of
x
3
x_3
is dependent on the value of
x
4
x_4
in the solution vector.
D
When
b
=
[
1
−
2
3
]
T
b=\begin{bmatrix}1&-2&3\end{bmatrix}^T
, the system has infinitely many solutions.
E
The system has
2
2
dependent and
2
2
independent variables.
