First slide

Applications of determinant

Question

The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0 is

Moderate

A

6
B

at least 7
C

less than 4
D

5

Solution

The matrix
$[\begin{array}{lll} 1 a b \\ c 1 d \\ e f 1 \end{array}]$
where exactly one of a, b, c, d, e, f is 1 and rest of them are zeros, is invertible.
There are six such matrices.
Also, the matrix $[\begin{array}{lll} 1 0 1 \\ 0 1 0 \\ 1 0 0 \end{array}]$ is invertible.
Thus, there are at least 7 such matrices which are invertible.

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