Question

A die was rolled 6 times and the results are displayed in matrix A. If the die rolls were repeated with the same results, which formula shows how to find the matrix that would display these results?

Answer 1

None of the above. (Ask your teacher to show you how to work this problem.)

Explanation:

Since the results are identical, the matrix of the next three rolls will look exactly like this matrix. (A)

The matrix of all 6 rolls will look like a 6-row matrix with the bottom 3 rows identical to the top 3 rows.

Adding or multiplying A by a constant will not produce these results.

_____

You can replicate columns using matrix multiplication, so you can transpose A, multiply it by a suitable version of an identity matrix, then transpose the result:

((A^T)·[I | I ])^T will turn the 3-row matrix to a 6-row matrix where I is a 3x3 identity matrix. I've used [I | I] here to mean the 3x3 identity matrix is itself replicated horizontally to make a 6-column matrix. ^T indicates transpose.