# Help with this puzzle?

Here is a set of problems that I encountered during an examination. Can anybody help me find the numbers where the '??' symbols are?

1. $\begin{bmatrix}10&6&2\\15&31&?? \\15&96&7 \end{bmatrix}$
2. $\begin{bmatrix}??&6&3\\22&27&43 \\27&108&29 \end{bmatrix}$
3. $\begin{bmatrix}36&??&45\\126&12&61 \\45&47&6 \end{bmatrix}$
4. $\begin{bmatrix}5&39&39\\41&10&34 \\120&??&30\end{bmatrix}$

I have no clue how to solve this, can anybody help?

• what replaces the question marks to make the determinate of these matrices equal to 1? – JonMark Perry Sep 19 '17 at 15:45
• it is the place where we need to fit suitable number – The Half Blood Prince Sep 19 '17 at 15:48
• What kind of exam? Linear algebra? – humn Sep 19 '17 at 15:54
• If this is math problem then why it is here? – paparazzo Sep 19 '17 at 16:33
• @Drt USS examination is for Kerala students (In INDIA) you can check it here, Here is the link... 103.251.43.156/lss_uss and I said 'I dont know further' means I dont wanna explain about it further.. Here people are making noises about examination not about Question – The Half Blood Prince Sep 25 '17 at 8:13

If this is an example of problems given on a USS exam in some part of Asia to identify gifted students then the object is probably to test them to see if they can figure the number to place where the ?? is to cause the

smallest value for the determinant of the given matrix.

If that is the case then the value for ?? in the first matrix is

4

and the value for ?? in the second matrix is

2

• ^vote with a note: Could use more explanation, including the fact that these numbers are rounded off. – humn Sep 20 '17 at 21:54