# Elementary row reduction for an $n\times n$ matrix

$$A= \begin{bmatrix} 1 & 1 & 1 & ... & 1 \\ 1 & 3 & 3 & ... & 3 \\ 1 & 3 & 6 & ... & 6 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & 3 & 6 & ... & 3(n-1) \end{bmatrix}$$

(a) Use the appropriate row replacement operations to zero out the first pivot then use the appropriate row replacement operations to zero out the second pivot column.

(b) Observe the resulting matrix from (a) is a block matrix of the form:

$$A = \begin{bmatrix} X & Y \\ 0 & Z \end{bmatrix}$$

State your resulting matrix for X, Y, and Z.

(c) Based on your result from (b), give a detailed set of steps to find $det(Z)$. [HINT: Take out a scaling factor for Z first then find $det(Z)$.]

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