"Let $$M = \left\{ {A = \left( {\matrix{ a & b \cr c & d \cr } } \right):a,b,c,d \in \{ \pm 3, \pm 2, \pm 1,0\} } \right\}$$. Define f : M $\to$ Z, as f(A) = det(A), for all A$\in$M, where z is set of all integers. Then the number of A$\in$M such that f(A) = 15 is equal to _____________."

Question

Accepted Answer

"| A | = ad $-$ bc = 15

where ${a,b,c,d \in \{ \pm 3, \pm 2, \pm 1,0\} }$

Case I ad = 9 & bc = $-$6

For ad possible pairs are (3, 3), ($-$3, $-$3)

For bc possible pairs are (3, $-$2), ($-$3, 2), ($-$2, 3), (2, $-$3)

So total matrix = 2 $\times$ 4 = 8

Case II ad = 6 & bc = $-$9

Similarly total matrix = 2 $\times$ 4 = 8

$\Rightarrow$ Total such matrices are = 16"

Let $$M = \left\{ {A = \left( {\matrix{ a & b \cr c & d \cr } } \right):a,b,c,d \in \{ \pm 3, \pm 2, \pm 1,0\} } \right\}$$. Define f : M $\to$ Z, as f(A) = det(A), for all A$\in$M, where z is set of all integers. Then the number of A$\in$M such that f(A) = 15 is equal to _____________.

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Let $$M = \left\{ {A = \left( {\matrix{ a & b \cr c & d \cr } } \right):a,b,c,d \in \{ \pm 3, \pm 2, \pm 1,0\} } \right\}$$. Define f : M $\to$ Z, as f(A) = det(A), for all A$\in$M, where z is set of all integers. Then the number of A$\in$M such that f(A) = 15 is equal to _____________.

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