Question

Explain to Carmine the significance of the zero matrix and the multiplicative identity matrix

Answer 1

See explanation below

Explanation:

The zero matrix is the matrix which has m rows and n columns and all its elements are zero, for example:

`\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]`

This matrix has the property that, when applied to a vector, sends it to zero.

On the other hand, the multiplicative identity matrix is an square matrix that has 1's in its diagonal and zero's everywhere else.

This matrix has the property that when multiplied by another one, doesn't change the first matrix (leaves things the same way as they were, it's like multiplying by one)

For example, a 3 x 3 multiplicative identity matrix would be:

`\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]`