3 A transformation T is represented by the matrix \(\mathbf { N } = \left( \begin{array} { l l l } a & 4 & 2
5 & 1 & 0
3 & 6 & 3 \end{array} \right)\), where \(a\) is a constant.
- Find \(\mathbf { N } ^ { 2 }\) in terms of \(a\).
- Find det \(\mathbf { N }\) in terms of \(a\).
The value of \(a\) is 13 to the nearest integer.
A shape \(S _ { 1 }\) has volume 11.6 to 1 decimal place. Shape \(S _ { 1 }\) is mapped to shape \(S _ { 2 }\) by the transformation T .
A student claims that the volume of \(S _ { 2 }\) is less than 400 . - Comment on the student's claim.