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Determinants and Elementary Row Operations (EROs)
Related Topics
Wize University Linear Algebra Textbook > Determinants
Determinants and EROs
3 Activities
If
A
=
[
a
b
c
d
e
f
g
h
i
]
A=\begin{bmatrix} a&b&c\\ d&e&f\\ g&h&i \end{bmatrix}
A
=
a
d
g
b
e
h
c
f
i
and
d
e
t
A
=
−
2
det\ A=-2
d
e
t
A
=
−
2
, find
d
e
t
[
g
h
i
2
d
−
a
2
e
−
b
2
f
−
c
a
b
c
]
det \begin{bmatrix} g&h&i\\ 2d-a&2e-b&2f-c\\ a&b&c \end{bmatrix}
d
e
t
g
2
d
−
a
a
h
2
e
−
b
b
i
2
f
−
c
c
.
-4
-2
-1
1
4
I don't know
Check Submission
More Determinants and EROs Questions:
133 - FML 3 - 18.1W e.g. 17.1
If
A
‾
\bcb{\boldsymbol{ \ul{A} }}
A
is a
3
×
3
\bcb{\boldsymbol{ 3 \times 3}}
3
×
3
matrix with
det
(
A
‾
)
=
−
4
\bcb{\boldsymbol{ \det{\ul{A}} = -4}}
det
(
A
)
=
−
4
, find:
det
(
2
A
‾
)
\boldsymbol{ \det {2\ul{A}}}
det
(
2
A
)
133 - FML 3 - 18.1W e.g. 9.3
Given that
∣
a
b
c
d
e
f
g
h
i
∣
=
−
3
\bcb{\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -3}
a
d
g
b
e
h
c
f
i
=
−
3
, find
∣
a
b
c
2
d
2
e
2
f
d
e
f
∣
{ \begin{vmatrix} a & b & c \\ 2d & 2e & 2f \\ d & e & f \end{vmatrix} }
a
2
d
d
b
2
e
e
c
2
f
f
133 - FML 3 - 18.1W e.g. 9.2
Given that
∣
a
b
c
d
e
f
g
h
i
∣
=
−
3
\bcb{\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -3}
a
d
g
b
e
h
c
f
i
=
−
3
, find
∣
3
a
3
b
3
c
g
+
3
a
h
+
3
b
i
+
3
c
2
d
2
e
2
f
∣
{ \begin{vmatrix} 3a & 3b & 3c \\ g + 3a & h+3b & i + 3c \\ 2d & 2e & 2f \end{vmatrix} }
3
a
g
+
3
a
2
d
3
b
h
+
3
b
2
e
3
c
i
+
3
c
2
f
133 - FML 3 - 18.1W e.g. 9.1
Given that
∣
a
b
c
d
e
f
g
h
i
∣
=
−
3
\bcb{\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -3}
a
d
g
b
e
h
c
f
i
=
−
3
, find
∣
−
a
d
2
g
−
b
e
2
h
−
c
f
2
i
∣
{ \begin{vmatrix} - a & d & 2 g \\ - b & e & 2h \\ -c & f & 2i \end{vmatrix} }
−
a
−
b
−
c
d
e
f
2
g
2
h
2
i
Determinants and EROs
A
=
[
a
b
c
p
q
r
x
y
z
]
,
B
=
[
4
x
4
y
4
z
p
+
x
q
+
y
r
+
z
a
b
c
]
A= \begin{bmatrix} a&b&c\\ p&q&r\\ x&y&z \end{bmatrix}, \quad B= \begin{bmatrix} 4x&4y&4z\\ p+x&q+y&r+z\\ a&b&c \end{bmatrix}
A
=
a
p
x
b
q
y
c
r
z
,
B
=
4
x
p
+
x
a
4
y
q
+
y
b
4
z
r
+
z
c
If
det
(
A
)
=
3
\det A=3
det
(
A
)
=
3
, find
det
(
B
)
\det B
det
(
B
)
.
Determinants and Elementary Row Operations (EROs)
Calculate determinant of
[
−
2
0
0
0
0
0
0
8
1
4
9
2
−
1
0
0
0
1
0
3
0
4
1
0
0
0
]
\begin{bmatrix} -2&0&0&0&0\\ 0&0&8&1&4\\ 9&2&-1&0&0\\ 0&1&0&3&0\\ 4&1&0&0&0\\ \end{bmatrix}
−
2
0
9
0
4
0
0
2
1
1
0
8
−
1
0
0
0
1
0
3
0
0
4
0
0
0
.
(Duplicated)
If it is known that
A
=
[
a
b
c
p
q
r
x
y
z
]
A= \begin{bmatrix} a&b&c\\ p&q&r\\ x&y&z \end{bmatrix}
A
=
a
p
x
b
q
y
c
r
z
and
d
e
t
(
A
)
=
5
det(A)=5
d
e
t
(
A
)
=
5
, determine
d
e
t
[
a
c
2
b
p
r
2
q
2
x
2
z
4
y
]
det \begin{bmatrix} a&c&2b\\ p&r&2q\\ 2x&2z&4y\\ \end{bmatrix}
d
e
t
a
p
2
x
c
r
2
z
2
b
2
q
4
y
.
Determinants and Elementary Row Operations (EROs)
If it is known that
A
=
[
a
b
c
p
q
r
x
y
z
]
A= \begin{bmatrix} a&b&c\\ p&q&r\\ x&y&z \end{bmatrix}
A
=
a
p
x
b
q
y
c
r
z
and
d
e
t
(
A
)
=
5
det(A)=5
d
e
t
(
A
)
=
5
, determine
d
e
t
[
2
a
2
b
2
c
p
−
3
x
q
−
3
y
r
−
3
z
p
q
r
]
det \begin{bmatrix} 2a&2b&2c\\ p-3x&q-3y&r-3z\\ p&q&r \end{bmatrix}
d
e
t
2
a
p
−
3
x
p
2
b
q
−
3
y
q
2
c
r
−
3
z
r
.