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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1950 AMC 12/AHSME
38
38
Part of
1950 AMC 12/AHSME
Problems
(1)
AHSME 1950- part 3
Source:
7/20/2008
If the expression
(
a
c
d
b
)
\begin{pmatrix}a & c \\ d & b \end{pmatrix}
(
a
d
c
b
)
has the value ab\minus{}cd for all values of
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
, then the equation
(
2
x
1
x
x
)
=
3
\begin{pmatrix}2x & 1 \\ x & x \end{pmatrix} = 3
(
2
x
x
1
x
)
=
3
:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
Is satisfied for only 1 value of
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
Is satisified for only 2 values of
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
Is satisified for no values of
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
Is satisfied for an infinite number of values of
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
None of these.
<span class='latex-bold'>(A)</span>\ \text{Is satisfied for only 1 value of }x \qquad\\ <span class='latex-bold'>(B)</span>\ \text{Is satisified for only 2 values of }x \qquad\\ <span class='latex-bold'>(C)</span>\ \text{Is satisified for no values of }x \qquad\\ <span class='latex-bold'>(D)</span>\ \text{Is satisfied for an infinite number of values of }x \qquad\\ <span class='latex-bold'>(E)</span>\ \text{None of these.}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
Is satisfied for only 1 value of
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
Is satisified for only 2 values of
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
Is satisified for no values of
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
Is satisfied for an infinite number of values of
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of these.
linear algebra
matrix