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Let the three digit numbers A28,3B9,62C where A, B, C are integers between 0 and 9 , be divisible by a fixed integer k. Show that the determinant A 3 6 8 9 C 2 B 2 is divisible by k

Let the three digit numbers A28,3B9,62C where A, B, C are integers between 0 and 9 , be divisible by a fixed integer k. Show that the determinant 
                                         
                                              A   3   6
                                              8   9   C  
                                              2   B   2
is divisible by k



Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
AsA28,3B9,62C where A, B, C are integers between 0 and 9 , be divisible by a fixed integer k then there exist m1,m2,m3 such that
100A+20+8=km1
300+10B+9=km2
600+20+c=km3
Applying R2=R2+100R1+10R2 we get
\Delta =\begin{bmatrix} A & 3 &6 \\ km1&km2 &km3 \\ 2& B & 2 \end{bmatrix}=kM
WhereM=\begin{bmatrix} A & 3 &6 \\ m1&m2 &m3 \\ 2& B & 2 \end{bmatrix}is an integer
Since A,m1,m2,m3,B are integers
Thus\Deltais divisible by k

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